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. speedofthewind:miles/hour

Answer 1

50 miles/hour

Explanation:

You want the speed of the wind if a 200 mph airplane can travel 500 miles with the wind in the same time as 300 miles against the wind.

Time

The travel time will be ...

t = d/r . . . . . where d is distance and r is rate of travel

t = 500/(200 +w) = 300/(200 -w) . . . . . where w is the wind speed

Cross multiplying and dividing by 100 gives ...

5(200 -w) = 3(200 +w)

1000 -5w = 600 +3w

400 = 8w . . . . . . . . add 5w-600

50 = w . . . . . . . . . . divide by 8

The speed of the wind is 50 miles/hour.

__

Additional comment

The speed with the wind is 250 mph, so 500 miles takes 2 hours. The speed against is 150 mph, so 300 miles takes 2 hours, the same time.

<95141404393>