• 500 New SAT Math Problems – Just 19.99 Today Only
    June 30, 2024

    500 New SAT Math Problems

    500 New SAT Math Problems
    Just 19.99 on Amazon

    Hi everyone! The latest edition of 500 New SAT Math Problems is now available in paperback from Amazon. This edition just has been modified from the previous edition to account for the changes on the Digital SAT.

    The paperback is now on sale on Amazon for only $19.99. Note that once the sale ends (by the end of today), the price of this book will go up to $42.99. 

    The promotion has ended. Thanks to everyone who participated. The book is now available at its regular price here: 500 New SAT Math Problems

    If you have any questions, feel free to contact me at steve@SATPrepGet800.com 

    Thank you all for your continued support!

    A Trick For Free Two Day Shipping

    I would like to finish this post with a little trick you can use to get free 2 day shipping on any of the books you decide to purchase without making any additional purchases. If you have never used Amazon Prime you can sign up for a free month using the following link.

    Sign Up For Amazon Prime For Free

    If you have already had a free trial of Amazon Prime you can simply open up a new Amazon account to get a new free trial. It just takes a few minutes! You will need to use a different email address than the one you usually use.

    This next part is very important! After you finish your transaction, go to your Account, select “Manage my prime membership,” and turn off the recurring billing. This way in a month’s time Amazon will not start charging you for the service.

    After shutting off the recurring billing you will still continue to receive the benefit of free 2 day shipping for one month. This means that as long as you use this new Amazon account for your purchases you can do all of your shopping on Amazon for the next month without having to worry about placing minimum orders to get free shipping.

    Just be aware that certain products from outside sellers do not always qualify for free shipping, so please always check over your bill carefully before you check out.

    Well I hope you decide to take advantage of this very special offer, or at the very least I hope you will benefit from my Amazon “free 2 day shipping trick.” Here is the link one more time:

    Sign Up For Amazon Prime For Free

    If you think your friends might be interested in this special offer, please share it with them on Facebook:

    Get 800 Facebook Share Button

    Thank you all for your continued support!

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  • Why I Use Bluehost To Host the Get 800 Website
    January 27, 2014

    Bluehost web hosting
    Hello everyone. I thought that it would be nice to change things up this week by talking about some of the aspects of my business I never thought I would be so involved with.

    It all started a few years ago when I decided to write my first SAT math prep book. Standardized test preparation was one of my areas of expertise and the first book I created far exceeded my expectations. What I didn’t realize at the time was that I would have to learn many other skills to actually sell my book. Since this business began I have learned website design including html, css, and javascript. I have learned all about social media such as Facebook, Twitter, Pinterest, YouTube and LinkedIn, and how important they can be for marketing. I’ve learned how to use wordpress, how to create lists in Aweber, and many more skills that I never even knew existed before. The last several months I have been working 14 hour days getting all of these pieces of my infrastructure to work together.

    Today I am giving you my very first technical post. I would like to talk about the web hosting company I use – Bluehost.

    For those of you unfamiliar with the expression “web hosting,” it’s quite simple. Websites need to be stored (or hosted) on a computer called a server. This server allows anyone in the world to reach your website. Your web files need to be uploaded to a server before people on other devices can find your website.

    Purchasing web hosting is just like renting an apartment except your web files “live” on the host’s server whereas you live in an apartment. A server is just like an apartment for your web files. Just like different apartments come with various amenities, hosting services may provide amenities as well such as disk space, email, design tools, and technical support.

    Why I Like Bluehost

    I have been using Bluehost as my provider since I have started my business. Here are some of the things I like about it:

    1. It’s very inexpensive – only $6.95 per month for basic service
    2. Your first domain name is free. If you only have one website, then this one free domain may be all you need. For example, my whole “Get 800” infrastructure is under the single domain SATPrepGet800.com.
    3. One account allows you to host unlimited domains. In other words if you ever do build another website you do NOT need to get a new Bluehost account. You can use the new domain under the same account. I currently have three domains under one Bluehost account (for example I just started the new domain ACTPrepGet36.com since I have just released my first ACT math prep book).
    4. They are available by phone 24/7 for technical support. Not only that, but every time I call with a technical issue or question I was on the line with someone in under 2 minutes. My issues are usually resolved very quickly. When I first started I would spend hours trying to fix everything that would go wrong myself – I didn’t realize that help was available for free. Now I just call up Bluehost and they can usually fix a problem in just a few minutes that might take me hours or days to solve.
    5. All your files AND databases are backed up daily at no extra charge. If something horrible goes wrong you can restore everything to how it was the day before.
    6. You get unlimited bandwidth and disk space. You can upload everything you need to run your website on an ongoing basis and they will never ask for more money.
    7. They are very WordPress friendly. I use WordPress for all of my domains, so for me this is important.

    Click here to visit Bluehost

    I hope that this information was helpful for those of you that are just finishing up your website deign and need a hosting service. Or maybe some of you are unhappy with your current hosting providers and want to switch.

    Next week I will be back with useful SAT prep information. See you then…

     
    Full Disclaimer: I have received no compensation from Bluehost. The opinions that I have shared are all my own. I take great pride in providing accurate, useful, and honest information to my audience.

    The links in this blog are affiliate links. If you click on one of these links and decide to sign up for a Bluehost account I will receive a commission on the sale. This does not cost you anything additional. 

  • New Get 800 Facebook Page For Your SAT Prep
    January 20, 2014

    Hello everyone. I would like to announce the new GET 800 Facebook Page.

    Yes, it’s true that I already have a Facebook page, but for several reasons I have decided to move it. Click the new Get 800 Facebook cover photo below to visit the new page. And while you’re there please don’t forget to press the like button.

    Get 800 SAT Prep Facebook Cover Photo

    And please use the button below to share the new page with your Facebook friends. They will thank you for it:

    Get 800 SAT Prep Facebook Share Button

    If you take a close look at the new Get 800 Facebook page you will notice some new tabs. You can now download free chapters from the Get 800 books, sign up for the free 12 part course (the 800 Initiation) and view (and purchase) right from Facebook any of the SAT math prep books from the Get 800 collection. In addition, you can click on the YouTube tab to view all of my SAT prep videos, click on the Twitter tab to view all of my latest tweets, and click on my Pinterest tab to view all of my Pinterest boards.

    As usual I will be posting lots of great SAT prep advice, tips, tricks, strategies, problems, and other important information regularly. But for the next month instead of posting weekly (as I have been), I will be posting every single day. And of course I will continue to answer all SAT related questions posted by you as quickly as I always have.

    So please visit the new Get 800 Facebook page, like it and share it.  Let’s all work together to get you a perfect score.

    I’ll see you on Facebook…

    Get 800 SAT Math Prep Facebook LinkGet 800 SAT Math Prep Twitter LinkGet 800 SAT Math Prep YouTube LinkGet 800 SAT Math Prep LinkedIn LinkGet 800 SAT Math Prep Pinterest LinkGet 800 SAT Math Prep Amazon LinkGet 800 SAT Math Prep Google+ LinkGet 800 SAT Math Prep Tumblr Link

  • SAT Math Strategy – Change Averages To Sums
    January 13, 2014

    Hello everyone.

    Today I would like to review a very important math strategy that can be used to solve SAT average problems of all difficulty levels very quickly. This strategy is “changing averages to sums.” I’ve already written a blog post on this subject here: Making SAT Math Problems With Averages Easy to Solve

    I have also just uploaded a video to my YouTube channel describing this strategy in detail. You can visit the YouTube page here: Change Averages To Sums

    The video is also embedded below for your convenience:

     

  • Guest Blog: The Six Things A Good SAT Vocab Flashcard Should Have
    January 6, 2014

    by Vince Kotchian

    If you’re serious about preparing for the SAT, you’re working on learning vocabulary on a daily basis. The sentence completion questions often come down to whether you know the words or not, and even the reading passages will test your vocabulary. Hopefully you’re treating learning vocabulary as learning, not memorizing. Not only will knowing the definitions of words help you for the SAT, but it will pay off in college and beyond. Hey, you speak English every day – you might as well know more of the language!

    One of the best ways to study vocabulary is by what I call a creative flashcard approach: “creative” – as opposed to “passive.” A passive approach is buying a box of cards and studying them. A more active approach is actually making your own cards. And this is important, because you’re more apt to remember something you’ve personally made.

    However, not all flashcards are created equal. A really useful flashcard has six important components:

    1. On one side of the card, write the word and nothing else.
    2. Write the word and a brief definition on the back in your words. By putting things into your own words, your brain has to process them more than just parroting a dictionary’s definition. But if you can’t put the definition into your own words without altering its meaning, use the dictionary’s.
    3. Write the pronunciation of the word in normal terms. By “normal”, I mean without using the symbols a dictionary would. For instance, if your word is PRODIGAL, your pronunciation might be PRA-DIG-UL. I want you to be able to pronounce the word because, on the days you’re studying it, you should try to use it at least once in conversation and once in writing.
    4. Come up with a mnemonic, or memory device, for the word. This is going to be another word or phrase that looks like or sounds like the word you’re trying to learn. For PRODIGAL, I like PRADA GAL. The definition of “prodigal” is “wasteful” – so picturing a “Prada gal” might remind you of that: a gal who buys Prada clothing, in the view of many, is wasting her money on expensive designer clothes.
    5. Write a sentence using the word and its mnemonic. For example, The PRODIGAL Prada gal spent her whole paycheck on a $1200 pair of boots. You want a sentence that is emotionally stirring or funny and one that is easy to visualize.
    6. Write some synonyms for the word, so you have other associations for it. M-w.com is a great resource for finding these.

    SAT Vocab Flashcard front

    SAT Vocab Flashcard Back

    Now, don’t worry too much if you can’t think of a clever mnemonic for every word. But try! I recommend trying to learn about 5 new words a day. Don’t forget to periodically review old words, too. Make a few piles of cards – the words you don’t know, the words you kind of know, and the words you definitely know. Your goal is to keep moving cards to the “know” pile. Don’t forget to review these once in a while, too, to make sure you still know all of them.

    I’ve written a vocab mnemonics book for the SAT – SAT Vocab Capacity – which is available on Amazon. Click the book image below to view the book on Amazon.

    SAT Vocab Capacity

    If you have any questions about vocabulary studying, feel free to contact me through my website, vincekotchian.com. Happy studying, and good luck on the SAT!

    -Vince Kotchian

    Vince Kotchian has been working full-time as a San Diego SAT, ACT, and GRE tutor since 2008. He combines a rigorous approach to teaching the foundational skills and techniques necessary for mastery with friendliness, patience, and adaptability. In addition to tutoring, Vince volunteers for a couple of causes: Promises2Kids – which helps foster youth pursue higher education – and Y.A.L.L.A., which helps refugee children. In his spare time, he likes to run, hike, play sports, and appreciate how nice it is to live in a place where he can walk outside without worrying about the weather.

  • Last Chance To Buy 1 Book and Get 6 FREE
    December 30, 2013

    Happy New year!

    This week I have written a guest article on Vince Kotchian’s Blog. You can read it here: SAT/ACT Math Strategies Every High School Student Should Know.

    More importantly , I want to remind you that this is your last chance to take advantage of the GET 800 holiday promotion. Simply use a link on this page to purchase ANY one of my test prep books in paperback from Amazon, and receive six free books from the GET 800 series as PDF files. This offer expires tomorrow, December 31, 2013.

    After purchasing any one book from Amazon in paperback that is displayed on this page, you will be provided with a link to download the following six books:









    Once again, here are the steps to get your six free books:

    1. Click on the picture of the book on this page that you would like to purchase in paperback and buy that book from Amazon (you can buy more than one if you choose, of course).
    2. Forward your Order Confirmation receipt to steve@SATPrepGet800.com with the subject line “Holiday Special.”

    That’s all! You will then receive an email with a link that will take you to a page where you can download all six books as PDF files.

    In addition to these six books you will receive two “Challenge Sets,” each consisting of 16 of my “Challenge Questions” specifically chosen to challenge more advanced students that are going for a perfect score on their standardized test. You will also receive a full study plan that explains exactly how to use all six of these books together. Please note that although you will be receiving a tremendous amount of material, you will only need to study for 10 to 20 minutes each day to drastically improve your SAT math score.

    To get the best price (and an additional book), you may want to purchase my ACT book in paperback. As of December 30, 2013 Amazon still has this book on sale for only $5.45. Please note that I have no control over Amazon’s discounts so this price can be raised back to $29.99 at any time. I apologize if the book is no longer on sale when you find this page. Click on the picture below to purchase the “ACT Prep Red Book.”




    It does not matter if you are taking the ACT or not. If you will be taking the ACT, keep the book. If not, simply give it as a gift to someone who is.

    And don’t forget to use my trick for free 2 day shipping by signing up for (and then cancelling) Amazon Prime.  If you have never used Amazon Prime you can sign up for a free month using the following link.

    Sign Up For Amazon Prime For Free

    If you have already had a free trial of Amazon Prime you can simply open up a new Amazon account to get a new free trial. It just takes a few minutes! You will need to use a different email address than the one you usually use.

    Remember to shut off recurring billing right after you finish your transaction! To do this, go to your Account, select “Manage my prime membership,” and turn off the recurring billing.

    After shutting off the recurring billing you will still continue to receive the benefit of free 2 day shipping for one month. This means that as long as you use this new Amazon account for your purchases you can do all of your holiday shopping on Amazon without having to worry about placing minimum orders to get free shipping.

    Just be aware that certain products from outside sellers do not always qualify for free shipping, so please always check over your bill carefully before you check out.

    By the way, Amazon Prime is actually a service you might even be interested in keeping, but I still recommend turning off recurring billing until you decide if you wish to keep it. You can always turn it back on.

    Well I hope you decide to take advantage of this very special holiday offer, or at the very least I hope you will benefit from my Amazon “free 2 day shipping trick.” Here is the link one more time:

    Sign Up For Amazon Prime For Free

    Once again, Happy Holidays!

  • Buy 1, GET 6 FREE
    December 23, 2013

    Happy Holidays everyone.

    I have decided to extend my holiday promotion until the end of the year. If you use a link on this page to purchase ANY one of my test prep books in paperback from Amazon, you will receive six free books from the GET 800 series as PDF files. This offer now expires on December 31, 2013.

    No, that was not a misprint. After purchasing any one book from Amazon in paperback that is displayed on this page, you will be provided with a link to download the following six books:









    Here are the steps to get your six free books:

    1. Click on the picture of the book on this page that you would like to purchase in paperback and buy that book from Amazon (you can buy more than one if you choose, of course).
    2. Forward your Order Confirmation receipt to steve@SATPrepGet800.com with the subject line “Holiday Special.”

    That’s all! You will then receive an email with a link that will take you to a page where you can download all six books as PDF files.

    In addition to these six books you will receive two “Challenge Sets,” each consisting of 16 of my “Challenge Questions” specifically chosen to challenge more advanced students that are going for a perfect score on their standardized test. You will also receive a full study plan that explains exactly how to use all six of these books together. Please note that although you will be receiving a tremendous amount of material, you will only need to study for 10 to 20 minutes each day to drastically improve your SAT math score.

    To get the best price (and an additional book), you may want to purchase my ACT book in paperback. As of December 23, 2013 Amazon still has this book on sale for only $5.45. Please note that I have no control over Amazon’s discounts so this price can be raised back to $29.99 at any time. I apologize if the book is no longer on sale when you find this page. Click on the picture below to purchase the “ACT Prep Red Book.”




    It does not matter if you are taking the ACT or not. If you will be taking the ACT, keep the book. If not, simply give it as a gift to someone who is.

    And don’t forget to use my trick for free 2 day shipping by signing up for (and then cancelling) Amazon Prime.  If you have never used Amazon Prime you can sign up for a free month using the following link.

    Sign Up For Amazon Prime For Free

    If you have already had a free trial of Amazon Prime you can simply open up a new Amazon account to get a new free trial. It just takes a few minutes! You will need to use a different email address than the one you usually use.

    Remember to shut off recurring billing right after you finish your transaction! To do this, go to your Account, select “Manage my prime membership,” and turn off the recurring billing.

    After shutting off the recurring billing you will still continue to receive the benefit of free 2 day shipping for one month. This means that as long as you use this new Amazon account for your purchases you can do all of your holiday shopping on Amazon without having to worry about placing minimum orders to get free shipping.

    Just be aware that certain products from outside sellers do not always qualify for free shipping, so please always check over your bill carefully before you check out.

    By the way, Amazon Prime is actually a service you might even be interested in keeping, but I still recommend turning off recurring billing until you decide if you wish to keep it. You can always turn it back on.

    Well I hope you decide to take advantage of this very special holiday offer, or at the very least I hope you will benefit from my Amazon “free 2 day shipping trick.” Here is the link one more time:

    Sign Up For Amazon Prime For Free

    Once again, Happy Holidays!

  • A Special Holiday Gift From Get 800
    December 16, 2013

    Hi all.

    This week Amazon has put some tremendous discounts on three of my books. Most of my books are usually priced at $29.99, but right now the Advanced Course from my “28 SAT Math Lessons” series is on sale for $9.48, “The 32 Most Effective SAT Math Strategies” is on sale for $9.80, and my new “ACT Prep Red Book” is on sale for $5.45. Please click on the pictures below to view each of these book’s Amazon product page.





    Please note that I have no control over Amazon’s discounts so I apologize if any of these discounts are gone by the time you see this blog post.

    Special Holiday Promotion

    In addition to these fantastic discounts, I am offering a very special deal for the holidays. If you use a link on this page to purchase ANY one of my test prep books in paperback from Amazon, you will receive six free books from the GET 800 series as PDF files. This offer expires on December 25, 2013.

    No, that was not a misprint. After purchasing any one book from Amazon in paperback that is displayed on this page, you will be provided with a link to download the following six books:









    Here are the steps to get your six free books:

    1. Click on the picture of the book on this page that you would like to purchase in paperback and buy that book from Amazon (you can buy more than one if you choose, of course).
    2. Forward your Order Confirmation receipt to steve@SATPrepGet800.com with the subject line “Holiday Special.”

    That’s all! You will then receive an email with a link that will take you to a page where you can download all six books as PDF files.

    In addition to these six books you will receive two “Challenge Sets,” each consisting of 16 of my “Challenge Questions” specifically chosen to challenge more advanced students that are going for a perfect score on their standardized test. You will also receive a full study plan that explains exactly how to use all six of these books together. Please note that although you will be receiving a tremendous amount of material, you will only need to study for 10 to 20 minutes each day to drastically improve your SAT math score.

    A Trick For Free Two Day Shipping

    I would like to finish this blog post with a little trick you can use to get free 2 day shipping on the book you decide to purchase without making any additional purchases. If you have never used Amazon Prime you can sign up for a free month using the following link.

    Sign Up For Amazon Prime For Free

    If you have already had a free trial of Amazon Prime you can simply open up a new Amazon account to get a new free trial. It just takes a few minutes! You will need to use a different email address than the one you usually use.

    This next part is very important! After you finish your transaction, go to your Account, select “Manage my prime membership,” and turn off the recurring billing. This way in a month’s time Amazon will not start charging you for the service.

    After shutting off the recurring billing you will still continue to receive the benefit of free 2 day shipping for one month. This means that as long as you use this new Amazon account for your purchases you can do all of your holiday shopping on Amazon without having to worry about placing minimum orders to get free shipping.

    Just be aware that certain products from outside sellers do not always qualify for free shipping, so please always check over your bill carefully before you check out.

    Well I hope you decide to take advantage of this very special holiday offer, or at the very least I hope you will benefit from my Amazon “free 2 day shipping trick.” Here is the link one more time:

    Sign Up For Amazon Prime For Free

    Have a happy and healthy holiday season!

  • New Book Covers For All GET 800 Products
    December 9, 2013


    GET-800-SAT-Prep-Books

    Hello everyone.

    I thought that this would be a good week to take a break from giving you  SAT math tips, tricks and tactics to show off my new book covers.

    Yes, I have spent the last several weeks redesigning each and every one of the covers for my seven SAT math prep books. If you want to learn more about these books, please visit the GET 800 product page.

    If you want to purchase any of these books, for your convenience you can do so right from this page. And now, let’s all take a look at the GET 800 books with their new covers.

     

    GET 800 “28 SAT Math Lessons” Series


    $29.99 $23.74

    $29.99 $24.00


    $29.99 $28.23

    $29.99 $24.00


    $29.99 $28.23

    $29.99 $24.00


    GET 800 SAT Math Workbooks


    $24.99 $23.74

    $29.99 $17.00


    $17.99

    $19.99 $5.00



     

    GET 800 SAT Math Strategy Guide and Solution Manual



    $29.99 $28.49

    $29.99 $17.00


    $29.99 $11.39

    $29.99 $24.00



    And for those of you that would like to see 2D versions of the new covers, here you go…

     


    New28BeginnerFrontCover


    New28BeginnerFrontCover


    New28BeginnerFrontCover


     


    New28BeginnerFrontCover

    New28BeginnerFrontCover




    32-Most-Effective-SAT-Math-Strategies-Front-Cover




    32-Most-Effective-SAT-Math-Strategies-Front-Cover



    Well I hope you enjoyed viewing  my new book covers. See you next week…

  • Can You Be Accused Of Cheating If You Show Significant Improvement on Your SAT or ACT?
    December 2, 2013

    Accused of Cheating

    Accused of Cheating?

    Who would ever think that a student could be punished for their hard work?  But the sad truth is that it happens. Most students do not even consider the possibility that they will be accused of cheating on a standardized test because they performed so well. But this situation does occur.

    Yes it is in fact true. The College Board has accused students of cheating on their SAT based only on their score increases from one SAT to the next (or from a student’s PSAT to his/her SAT).

    If you are accused of cheating on the SAT, the College Board will most likely cancel your scores and ask you to retake the test in a private setting.

    Now nobody likes being accused of cheating, and nobody wants to retake a four hour exam. But that’s not even the worst part. By the time you are asked to retake the test it may have been a long while since you last prepared for the exam. You may not do as well simply because you are out of practice. You thought that this long, arduous test was finally over and now you have to go through the whole process again.

    And by the way, this is not unique to the SAT. This happens with the ACT as well. I actually had a student that was already in college on a scholarship while the ACT was threatening to cancel her scores. The case went into arbitration. If the ACT had won, the student would have had to pay back all of her scholarship money. As the student’s ACT tutor I had to testify in her defense.

    How can you protect yourself?

    Well if you have spent a lot of time preparing properly for the SAT (or ACT) and you expect your score to go up several hundred points from the last time you took the test, you may want to take the following two precautions:

    (1)    Show additional work in your test booklet even if you do not need to.

    (2)    Try to be certain of your answers before you bubble them in so you do not produce too many erasure marks.

    Yes I do realize that the test makers are not supposed to be looking at your work in your test booklet, and I also realize that there is not supposed to be a penalty for changing your answers after checking them over. But these two key pieces of “evidence” can be used against you in a hearing. Indeed, they have been used as evidence of cheating by prosecutors in the past.

    Also, if you take the above two precautions, it is less likely that you will be accused of cheating to begin with. An extremely large score increase will possibly set off a flag that the test makers will want to investigate.  But they may not immediately accuse you of cheating before looking over your results carefully. If they are convinced from your test booklet that you knew what you were doing, then you will most likely be left alone.

    By the way, if you happen to use my test prep materials, you will probably notice that for many problems you do not need to show much work in your test booklet at all. Many of the techniques I teach are designed to solve problems very quickly and with little to no writing. Nonetheless, if you feel like your score is going to improve several hundred points from your last test, please show some work in your test booklet anyway.

    One might then ask “Does spending extra time writing in the test booklet negate the positive effects of using my time-saving strategies to begin with?”

    My answer is “no.” First of all, the advice in this article is only for students that believe they will go up at least 400 total points from their last SAT (by total points, I mean 400 points across all three sections – math, reading and writing). Second, if you happen to be one of these students, then your skill level has improved so much that it should not affect your score at all to scribble a little extra work in your test booklet.

    So please continue to prepare, and do the best that you can when you take your test, but be a little extra cautious if you are expecting a very large score increase.

    If you liked this article, please share it with your Facebook friends:

    SAT Math Facebook Share Button

    I’ll see you next week!

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  • More SAT Math Problems Involving Distance, Rate And Time
    November 18, 2013

    d=rtWelcome back. Last week we discussed how to solve a certain type of rate problem very quickly simply by plugging numbers into a simple formula. In case you are interested you can find that post here: Xiggi’s formula.

    In last week’s post we learned that Xiggi’s formula can be used to find an average rate when two individual rates for the same distance are known.

    But what if we want to find the distance or time instead?

    If the two distances are the same, then Xiggi’s formula can still be used but the solution will require a little more work. In this case however Xiggi’s formula is probably not the most efficient way to solve the problem.

    Also, what if we want to solve a rate problem where the two (or more) distances are different?

    Well in this case we certainly cannot use Xiggi’s formula. Another method will be needed.

    In this blog post I would like to go over a method of solution that will work for any SAT math problem involving distances, rates and times. Today we will carefully go over how to set up a “distance = rate · time” chart.

    Let’s start right away with an example.

    drivingMarco drove from home to work at an average speed of 50 miles per hour and returned home along the same route at an average speed of 46 miles per hour. If his total driving time for the trip was 4 hours, how many minutes did it take Marco to drive from work to home?

    Let’s solve this problem by writing out a “distance = rate · time” chart.

      ________________   _Distance                  Rate                       Time
    home to work                d                            50                          d/50
    work to home                d                            46                          d/46
    total                                                                                                  4

    Note that although we do not know either distance, we do know that they are the same, so we can call them both “d.” Also, since

    distance = rate · time,

    we have that

    \text{time} = \frac{\text{distance}}{\text{rate}}.

    We use this to get the first two entries in column three. The total time is given in the question. So we have

    \frac{d}{50} + \frac{d}{46}=4

    46d + 50d  = 4 · 50 · 46

    96d = 4 · 50 · 46

    d = \frac{4 \cdot 50 \cdot 46}{96}

    We want the time it takes Marco to drive from work to home, that is we want to compute d/46.

    In hours, this is equal to

    \frac{d}{46} = \frac{4 \cdot 50}{96}

    To convert to minutes we multiply by 60.

    \frac{d}{46} = \frac{4 \cdot 50 \cdot 60}{96} = \bf{125} \ \text{minutes}

    Let’s also try to solve this problem using Xiggi’s formula. We have

    \text{Average speed} = \frac{2(50)(46)}{50+46} = \frac{575}{12}.

    \text{So total round trip distance} = r\cdot t = \frac{575}{12} \cdot 4 = \frac{575}{3}.

    \text{So distance from work to home} = \frac{575}{3} \div 2 = \frac{575}{6}.

    \text{So time from work to home} = \frac{d}{r} = \frac{575}{6} \div 46 = \frac{25}{12}.

    Finally to convert from hours to minutes we multiply by 60 and get 125.

    Notice that this particular problem was not so straightforward to solve using Xiggi’s formula. Compare this to the problem in last week’s blog post. Do you see the difference? In last week’s question we were being asked to find a rate, whereas in this question we were asked to find a time.

    Toward the end of last week’s post you were asked to solve the following problem:

    runnerJason ran a race of 1600 meters in two laps of equal distance. His average speeds for the first and second laps were 11 meters per second and 7 meters per second, respectively. What was his average speed for the entire race, in meters per second?

    Let’s first solve this problem using Xiggi’s formula.

    \text{Average speed} = \frac{2(11)(7)}{11+7} = \frac{154}{18} \sim 8.555555.

    So we can grid in 8.55 or 8.56.

    And now here is a solution using a “distance = rate · time” chart.

      ________________   _Distance                  Rate                       Time
    lap 1                       800                            11                          72.727
    lap 2                       800                             7                           14.286
    total                      1600                                                        187.01

    \text{Average speed} = \frac{\text{distance}}{\text{time}} \sim \frac{1600}{187.01} \sim 8.555555.

    So we grid in 8.55 or 8.56.

    Now go find some more difficult rate problems to practice. You can always find lots of problems in my GET 800 SAT math prep books.