Craig can ride his bike at an average rate of 14 miles per hour in calm air. Traveling with the wind, he rode his bike 62 miles in the same amount of time it took him to ride 50 miles against the wind. Find the speed of the wind.

Question

Graves

Mathematics

6 December, 16:40

Craig can ride his bike at an average rate of 14 miles per hour in calm air. Traveling with the wind, he rode his bike 62 miles in the same amount of time it took him to ride 50 miles against the wind. Find the speed of the wind.

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Answers (1)

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Small · Answer 1

Answer: the speed of the wind is 1.5 mph

Step-by-step explanation:

Let x represent the speed of the wind.

Time = distance/speed

Craig can ride his bike at an average rate of 14 miles per hour in calm air. Traveling with the wind, his total speed would be (14 + x) mph

Time taken to travel 62 miles with the wind would be

62 / (14 + x)

In the same amount of time it took him to ride 50 miles against the wind. His total speed would be

(14 - x) mph. Time taken to travel 50 miles is

50 / (14 - x)

Since the time is the same, then

62 / (14 + x) = 50 / (14 - x)

Cross multiplying, it becomes

62 (14 - x) = 50 (14 + x)

868 - 62x = 700 + 50x

- 62x - 50x = 700 - 868

- 112x = - 168

x = - 168/-112

x = 1.5