Word problem

Question

A plane has a cruising speed of 100 miles per hour when there is no wind. At this speed, the plane flew
600 miles with the wind in the same amount of time it flew 400 miles against the wind. Find the speed of the wind.

 

What is the speed of the wind?

Answer 1

Let x = speed of wind

 

Speed of plane with the wind = x + 100

Speed of plane against the wind = 100 -x 

 

Distance = (Rate)(Time)   So, Time = distance/rate

 

Time to travel 600 miles with the wind = Time to travel 400 miles                                                                                             against the wind

 

600/(x + 100) = 400/(100 - x)

 

400(x + 100) = 600(100 - x)

 

400x + 40000 = 60000 - 600x

 

1000x = 20000

 

x = 20 mph