Official Guide Explanation:
Problem Solving #142

Background

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Solution and Metadata

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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