Official Guide Explanation:
Problem Solving #119

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Solution and Metadata

Question: 119
Page: 77
Difficulty: 6 (Moderately Difficult)
Category 1: Word Problems > Rate Problems > Combined Rate

Explanation: To find the the point in the middle where trains X and Y met requires first finding the rate for each train. Train X traveled 100 miles in 5 hours, for a rate of (100/5) = 20 miles per hour. Y traveled 100 miles in 3 hours, for a rate of (100/3) = 33(1/3) miles per hour. Combined, the trains moved toward each other at a rate of 53(1/3) miles per hour. Next, find out how long it took for the trains, combined, to travel 100 miles: 53(1/3) = (100/(t)), or 53(1/3)(t) = 100, or t = (100/(53(1/3))) = (300/160) = (30/16) = (15/8) hours. In other words, when the trains meet, they each had been traveling for (15/8) hours. So, at that point, train X's distance was given by (rate)(time) = (20)((15/8)) = 5((15/2)) = (75/2) = 37.5, choice (A).

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