Question

A boater travels 39 miles per hour on the water on a still day. During one particularly windy​ day, he finds that he travels 26 miles with the wind behind him in the same amount of time that he travels 13 miles into the wind. Find the rate of the wind.

Answer 1

Answer-

The speed of wind is 13 mph

Solution-

We know that,

$Speed =\frac{Distance}{time}$

⇒ $Time=\frac{Distance}{Speed}$

Let's assume, W = speed of wind  

39 + W = speed with the wind  

39 - W = speed against the wind

Time taken by him to travel with the wind $=\frac{26}{39+W}$

Time taken by him to travel against the wind $=\frac{13}{39-W}$

∴ As he takes same time for both the cases

⇒ $\frac{26}{39+W} = \frac{13}{39-W}$

⇒ 78 - 2W = 39 + W

⇒ 3W = 39

⇒ W = 13 mph