Xiggi's Formula – An Advanced Math Strategy

Xiggi’s Formula – An Advanced Math Strategy

Hello everyone. This post is mostly for more advanced students that are trying to get an 800 in SAT math (or close to it). That said, the strategy I will be describing here is actually very easy to apply. So even if you are not going for an 800, it will not take too much effort to learn this technique.

Today I would like to talk about Xiggi’s formula.

First of all, some of you may want to know who Xiggi is. Well Xiggi is a frequent poster on the SAT preparation forum of College Confidential. If you are preparing for the SAT I highly recommend that you utilize this forum as a resource.

The formula I will be discussing in this post is actually called the harmonic mean formula, but on the College Confidential site we all call it Xiggi’s formula. The reason for this is because Xiggi has become well known for helping students on the forum to solve this particular type of problem.

So when should one use Xiggi’s formula? Well, Xiggi’s formula can be used to find an average rate when two individual rates for the same distance are known.

Here is the formula:

$\text{Average speed} = \frac{2(\text{speed} 1)(\text{speed} 2)}{\text{speed} 1 + \text{speed} 2}$

Important notes: (1) Xiggi’s Formula works only when the two distances are the same.

(2) Even though the distance is often given in these types of problems, note that the formula does not use the distance. It uses only the two rates.

(3) For these types of SAT problems, the words “rate” and “speed” are interchangeable.

Here is an example of a problem where Xiggi’s formula is the best way to go:

An elephant traveled 7 miles at an average rate of 4 miles per hour and then traveled the next 7 miles at an average rate of 1 mile per hour. What was the average speed, in miles per hour, of the elephant for the 14 miles?

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

$\text{Average speed} = \frac{2(4)(1)}{(4+1)} = \bf{\frac{8}{5}} \text{ or } \bf{1.6}.$

Just to compare, let’s also solve this problem in the more traditional way – by writing out a “distance = rate · time” chart.

d=rt chart

Note that we computed the times by using “distance = rate · time” in the form $\text{time} = \frac{\text{distance}}{\text{rate}}.$

Finally, we use the formula in the form

$\text{rate} = \frac{\text{distance}}{\text{time}} = \frac{14}{8.75} = \bf{1.6}.$

Note: To get the total distance we add the two distances, and to get the total time we add the two times. Be careful – this doesn’t work for rates!

SAT, ACT and GRE math problems of this type are always Level 5 problems. But if you know Xiggi’s formula, you can solve this type of question in just a few seconds. So in my opinion, it is well worth committing this one to memory.

Here is another math question where Xiggi’s formula can be useful. Give this one a try on your own.

Jason 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?

See if you can solve this problem using Xiggi’s formula. And then also try to solve it with a “distance = rate · time” chart.

I will provide both solutions in tomorrow’s post. But feel free to leave your own solutions in the comments.

Remember that Xiggi’s formula should only be used when the two distances are the same! Should it ALWAYS be used when the distances are the same? We will address this question in next week’s post where we will look at distance, rate, time problems where Xiggi’s formula is not as useful.

Until then, I will leave you with the following “Challenge Problem.”

Use the formula d = rt to derive Xiggi’s formula.

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Xiggi’s Formula – An Advanced Math Strategy

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