help solving this word problem

Question

i need help to solve this word problem; "an airplane can travel 220 miles with the wind speed in the same amount of time it can travel 175 miles against the wind. if the speed of the plane in till air is 100 mph then what is the speed of the air?"

Answer 1

Let x = wind speed

 

Speed of plane with the wind = x+100

Speed of plane against the wind = 100-x

 

Distance = (Rate)(Time), so Time = Distance/Rate

 

Time with the wind = Time against the wind

 

So, 220/(x+100) = 175/(100-x)

 

Cross multiply to get 220(100-x) = 175(x+100)

 

Divide by 5:  44(100-x) = 35(x+100)

 

                     4400 - 44x = 35x + 3500

 

                               79x = 900

 

                                  x ≈ 11.4 mph