First post!

Hi and welcome to the first post of the SAT Math Explanations Blog! Here, I'll try to offer explanations to the more difficult SAT math questions. Feel free to mail me (SAT.math.section@gmail.com) any math questions you need explanations for. I'll try to answer as many as possible. I don't care whether they're from previously administered tests, from the Official SAT Question of the Day or from any other source, as long as they present topics that are covered on the SAT. So fire away!

The following question is from the Offical SAT Question of the Day series by Collegeboard. According to their statistics 65% answered incorrectly. Let's take a look at it:

A woman drove to work at an average speed of 40 miles per hour and returned along the same route at 30 miles per hour. If her total traveling time was 1 hour, what was the total number of miles in the round trip?

1. Let's call the number of miles in one direction x. Therefore, our final solution will be 2x. That's important to remember.
2. It is given that the total time was 1 hour, so one side of our equation will be 1 hour:
   1h = ?
3. We need to have the same quantity (the same "type" of something) on the other side of the equation, i.e. we need something in hours. Therefore, we need to "convert" the mph into hours. We don't know the number of miles in one direction, but we have defined it as x. We can now express the time it took in terms of x. If we need 1h for 40miles, how long does it take when we drive x miles?
   40miles -->:40 *x --> x
   1 hour -->:40 *x --> x/40
   It takes x/40 hours. We have now expressed the time in terms of x.
4. The same holds true for 30mph, except that it now takes x/30 hours. Therefore, x/40 + x/30 is the total time:
   1h = x/40 + x/30
5. Solving the equation yields 17 1/7 for x. Therefore, the total number of miles is:
   2 * 17 1/7 = 34 2/7

This type of question is quite common on the SAT, by the way.