Question

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

Answer 1

The speed of the wind is 50 miles per hour.

What is speed?

The term speed is defined as the ratio of the distance to the time taken. Now we can see that the movement of the plane and the wind were once in the same direction and then in opposite direction. This could be used to obtain a pair of simultaneous equations that could be used to solve the problem.

Hence;

300 = (250+s)* t = 250t + st ----- (1)

200 = (250-s)* t = 250t   - st  ------- (2)

Adding equations (1) and (2)

500 = 500t

t = 1 hour

To obtain the speed of the wind;

300 =250t + st

300 = 250(1) + (s * 1)

300 = 250 + s

300 - 250 = s

s = 50 miles per hour

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Missing parts;

A plane has a cruising speed of 250 miles per hour when there is no wind. At this speed, the plane flew 300 miles with the wind in the same amount of time it flew 200 miles against the wind. Find the speed of the wind.