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## Official Guide Explanation:Problem Solving #142

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Quantitative Review (2nd 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: 142
Page: 80
Difficulty: 6 (Moderately Difficult)
Category 1: Word Problems > Rate Problems > Speed
Category 2: Word Problems > Rate Problems > Combined Rate

Explanation: To start, focus on the entire trip. The goal is to drive a total of 40 miles at an average speed of 60 miles per hour. Using the rate formula:

r = ((d)/(t))

60 = (40/(t))

t = (40/60) = (2/3) of an hour, or 40 minutes.

The first part of the trip was 20 miles at 50 miles per hour: use the rate formula again:

r = ((d)/(t))

50 = (20/(t))

t = (20/50) = (2/5) of an hour, or 24 minutes.

Thus, the second 20 miles must happen in 16 minutes, which is (16/60) = (8/30) = (4/15) of an hour.

Again, go to the rate formula, know the distance is 20 and the time is (4/15):

r = (20/((4/15)))

(4/15)r = 20

r = (15/4)(20) = 75

That's the necessary speed for the second 20 miles, so choice (D) is correct.

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