Question

A plane has a cruising speed of 200 miles per hour when there is no wind. At this speed, the plane flew 500 miles with the wind in the same amount of time it flew 300 miles against the wind. Find the speed of the wind.

Answer 1

Answer:

Speed of wind is 380 miles per hour.

Explanation:

Case 1) When no wind is flowing:

Using the basic relations of distance speed and time we have

$Time=\frac{Distance}{Speed}\\\\\therefore Time_{nowind}=\frac{500}{200}=2.5hrs$

When the plane moves against the wind it's effective speed reduces as it has to overcome the opposing force of the wind since it is given that it cover's a distance of 300 miles in the same time we can write

$2.5=\frac{300}{V_{plane}-v_{wind}}\\\\2.5=\frac{300}{500-v_{wind}}\\\\500-v_{wind}=\frac{300}{2.5}\\\\\therefore v_{wind}=500-\frac{300}{2.5}\\\\v_{wind}=380mph$