SOLUTION: A biker rides 106 miles in 6 hours against the wind. He rides 126 miles in 6 hours with the wind at his back. What is the speed of the wind?

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Question 352481: A biker rides 106 miles in 6 hours against the wind. He rides 126 miles in 6 hours with the wind at his back. What is the speed of the wind?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Let b = speed of the biker
w = speed of the wind.
This means b - w = speed of the biker relative to, and against, the wind
Because d+=+r%2At, we get 6%2A%28b-w%29=106, or b-w=53%2F3.
Also, b + w = speed of the biker relative to, and in the same direction as, the wind. So
6%2A%28b%2Bw%29=126, or b%2Bw=21. So we have the system
b-w=53%2F3, and
b%2Bw=21.
Solving this by elimination gives
b=58%2F3 and w=5%2F3.
Therefore the speed of the wind is 5/3 miles per hour.