Question

Alicia’s average speed riding her bike is 12 miles per hour. She goes from her house in a straight line against the wind to the beach, and then in a straight line with the wind back to her house, totaling 40 miles in 4 hours. What is the speed of the wind?

Answer 1

Speed of wind is 4.90 miles per hour

Explanation:

Let the speed of wind be w.

Alicia’s average speed riding her bike = 12 mph

Speed against wind = 12 - w

Speed with wind = 12 + w

Total distance traveled = 40 miles

Total time taken = 4 hours

Distance to beach is half of the distance traveled which is 20 miles

We have

        $\frac{20}{12-w}+\frac{20}{12+w}=4\\\\\frac{5}{12-w}+\frac{5}{12+w}=1\\\\60+5w+60-5w=144-w^2\\\\w^2=24\\\\w=4.90mph$

Speed of wind is 4.90 miles per hour