Official Guide Explanation:
Problem Solving #206

Background

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Solution and Metadata

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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