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?

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) (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 , we get , or .
Also, b + w = speed of the biker relative to, and in the same direction as, the wind. So
, or . So we have the system
, and
.
Solving this by elimination gives
and .
Therefore the speed of the wind is 5/3 miles per hour.
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