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2018 Official Guide to the GMAT Review Series: Problem #23 (Algebra Distance-Rate Problems)

Posted by John Easter on August 31, 2018 2:43:00 PM CDT

GMAT math distance-rateThis post is the fourth in our series on using strategies to answer specific questions from the 2018 Official Guide. Here, one of our most experienced GMAT tutors, John Easter, analyzes a question about distance-rate.

During a certain time period, Car X traveled north along a straight road at a constant rate of 1 mile per minute and used fuel at a constant rate of 5 gallons every 2 hours. During the time period, if Car X used exactly 3.75 gallons of fuel, how many miles did Car X travel?

(A) 36

(B) 37.5

(C) 40

(D) 80

(E) 90

This is a basic distance-rate problem, but the standard D = RT table isn't very convenient here. Before I jump in, I'm going to do some estimation/approximation and see if I can eliminate some of the answer choices.

First, 1 mile per minute = 60 miles per hour. Second if 5 gallons is equivalent to 2 hours of travel, 3.75 gallons will be more than one hour (it's more than half of 5 gallons). So, Car X has obviously gone more than 60 miles. A, B, and C are out.

Now if I round 3.75 gallons to 4 gallons, then the corresponding travel time will be 4/5 of 2 hours = 4/5(2) = 8/5 hours. At 60 miles per hour, that's 60(8/5) = 96 miles

Because I rounded up, this should be slightly larger than the exact distance.

The correct answer is E.

If that's a little bit too seat-of-the-pants for you, we can use a proportion and solve for the exact amount of travel time:

3.75/5 = x/2

(2)(3.75) = 5x

And x equals 7.5/5 = 15/10 = 3/2. So 1.5 hours at 60 miles per hour is exactly 90 miles.

 

About the Author

John Easter is one of MyGuru’s longest tenured and most experienced GMAT tutors. He is also the founder of Owl Test Prep, another great source for GMAT advice.

 

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