Question 275984
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These kinds of problems are intended as mathematical exercises, without concern for the physics.<br>
In this problem, the speed of the cyclist against the wind is 30/3 = 10 mph and with the wind is 80/5 = 16 mph.<br>
You can solve the problem using formal algebra:
c the speed of the cyclist in still air
w the speed of the wind
c+w=16; c-w=10  -->  c=13, w=3<br>
But an informal solution using logical reasoning is much easier: the speed of the cyclist is halfway between his speed with the wind and his speed against the wind:
(10+16)/2 = 13
and the speed of the wind is the difference between that speed and either of the other speeds:
16-13 = 3 mph, or 13-10 = 3 mph<br>
ANSWERS: cyclist 13 mph; wind 3 mph<br>