Bunuel wrote:
Johnny travels a total of one hour to and from school. On the way there he jogs at 5 miles per hour and on the return trip he gets picked up by the bus and returns home at 20 miles per hour. How far is it to the school?
A. 2 miles
B. 4 miles
C. 4.8 miles
D. 8 miles
E. 10 miles
Kudos for a correct solution.
PRINCETON REVIEW OFFICIAL SOLUTION:What is the question asking?The question is looking for a distance that Johnny travels. Good news for us. All the answer choices are in miles.
Where are you starting?I have two rates of travel and a total time to apportion to and from the school. Let me suggest that there are many ways to attack this one. I will offer just a few to demonstrate that multiple methods lead to the same spot.
A) The Algebra Student says: I will work with the rates and I can see that one is four times the other in terms of time, because D=R*T (Distance = Rate X Time). I know they are inversely related. So 5T= 1 hour. Therefore T=.2 hours. I can take either the bus speed or the bicycle speed and plug in: 20 miles an hour multiplied by .2 hours results in 4 miles. We check the work and we are right.
B) The Plug-In Master says, let me try each of the distances and see what I get. So he starts at 4.8 miles and divides that by 4 miles per hour and recognizes that he is already over an hour time, tries 4 miles and the math works.
C) The Class Math Wiz tells us that there is an elegant way to take the reciprocal of the rates, add them together, flip that result over and voilá we get 4 miles. While our Wiz is absolutely correct, we all shake our heads and look for something that we all can use.
D) Finally, our Class Ball Parker says that all of this was unnecessary, because we only had an hour available to us for both jogging and the bus. Since this is true, we exclude answers C, D, and E. They are too big. We look at 2 miles and realize it is too small and won’t even come close to totaling one hour and without any math, arrive at the exact same answer.
I guarantee that there are even more ways to attack this one problem. Which method is the best? There really is no answer to that. As a student taking the GMAT you really have to determine for yourself which method works for you. However, the first step is to understand where you are starting and where you are going. You need to know exactly what you are looking for, and what tools and information you have available to help you get to the answer.
This is why it is crucial to work as many problems in your practice tests as possible. The more familiar you are, both with the math and the way in which the questions are presented, the better the chances for success.
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