You ride your bike to a store, 4 mi away. When there is no wind, you ride at 10 mi/h. Today your trip to the store and back took 1 hour. What was the rate of the wind today?

Question

I’ve tried to use the r=dt and I haven’t been able to find the right answer.

Answer 1

If the speed of the wind is w mph, the overall speed with the wind is 10+w and against it is 10-w.

The time taken to ride 4 miles in each direction is 4/(10+w)+4/(10-w)=1 because time=distance/speed.

Multiply through by (10-w)(10+w): 4(10-w)+4(10+w)=100-w².

So 40+40=100-w², w²=20, w=√20=2√5=4.472 mph.