SAT Math Multiple Choice Practice Question 116: Answer and Explanation

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Question: 116

6. Biking with the wind, a cyclist took 40 minutes to complete a ride. Biking against the wind, the cyclist took 60 minutes to complete the same ride. Assuming that the cyclist bikes 30 miles per hour without any wind, and that the wind's speed was constant, the speed of the wind, in miles per hour, was

A. 5
B. 6
C. 8
D. 10
E. There is not enough information given.

Correct Answer: B


B. Let the wind's speed equal x. Because the cyclist bikes 30 miles per hour without any wind, his speed was 30 + x with the wind, and 30 - x against the wind. With the wind, the trip took 40 minutes, but you have to convert this to 2/3 of an hour because you're measuring speed in miles per hour. Similarly, against the wind, the trip took one hour exactly. The distance was the same both times, and distance equals speed times time. Bingo: 2/3(30 + x) = 1(30 - x). Distributing gives you 20 + (2/3)x = 30 - x, and regrouping gives you (5/3)x = 10. Finally, you can multiply both sides by 3/5, and x = 6. As befits the last problem in the section, this one is pretty hard!

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