11.23.14
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Do this SAT problem the EASY way!

So you ‘don’t know how’ to do this SAT Question of the Day? http://sat.collegeboard.org/practice/sat-question-of-the-day?questionId=20141121&oq=1 The explanation given on the SAT site (look please!) is a good one, but ONLY if you would have thought of it! That’s the way your Algebra teacher wants you to do the problem. But DON’T SKIP IT! Do it MY WAY!
                                        

Q: 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?

                          

 
There’s always a way to get rid of a choice or two. Let’s look…

 

(A) 30

(B) 30 1/7

(C) 34 2/7

(D) 35

(E) 40

Is it 30? No. Driving a distance of 30 miles in a total of 1 hour would give an overall average speed of 30 miles per hour. 30 mi/hr is the average speed for the second part of the trip, but the speed for the first part is 40 mi/hr. So, the overall average speed would be somewhere between 30 and 40, and therefore the number of miles would be between 30 and 40. (We’re talking about 1 hour, so the speeds and the distances will be the same numbers.) Cross out choice (A). Also cross out choice (E) for the same reason.

You’re down to three choices. At this point if you just guessed, you stand to gain more than you would lose. But you can do even better. The (wrong) answer they want you to fall for is (D). It’s too easy. It’s not just the average of 30 and 40, since the times spent at 30 vs 40 miles per hour are different. Cross out choice (D).

Two choices left. You were convinced above that 30 was the wrong answer. 30 1/7 is too close to 30 to make that big of a difference. The extra 1/7 of a mile wouldn’t be enough to raise the average speed to 40 for the first part of the trip. Cross out choice (B).

Done. The answer is C.

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