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Official Guide Explanation:Problem Solving #206

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Review (12th ed.). Click the links on the question number, difficulty level, and categories to find explanations for other problems.

These are the same explanations that are featured in my "Guides to the Official Guide" PDF booklets. However, because of the limitations of HTML and cross-browser compatibility, some mathematical concepts, such as fractions and roots, do not display as clearly online.

Question: 206
Page: 181
Difficulty: 7 (Very Difficult)
Category 1: Word Problems > Rate Problems > Speed
Category 2: Word Problems > Rate Problems > Combined Rate
Category 3: Algebra > Linear Equations-One Unk >

Explanation: The only rate that matters in a problem like this is the difference between the two rates. If car A is traveling at 58 miles per hour and car B is traveling at 50 miles per hour, the difference is 8 miles an hour. Put another way, if the two cars drove along the same route for an hour, car A would be 8 miles further, and would do the same for each subsequent hour. Since the question wants to know how long it will take for car A to make up a 20 mile difference and get 8 more miles ahead, we want to know how long it will take for something happening at a rate of 8 miles per hour to cover 28 miles. We can turn to the rate formula: if r = ((d)/(t)), then

8 = (28/(t))

8t = 28

t = (28/8) = (7/2) = 3.5, choice (E).

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