solve word problem

Question

a plane can fly 2000 miles with a tailwind in 4 hours. it can make the return trip against the same wind in 5 hours. find the speed of the plane in still air and the speed of the wind

Answer 1

2000 = (r+s)*4

 

2000 = (r-s)*5

 

Subtracting the 1st equation from the second:

 

 (r-s)*5 - (r+s)*4 = 0

 

5r - 5s - 4r - 4s = 0

 

r -9 s = 0

 

r = 9s

 

The plane is 9 times as fast as the wind.

 

2000 = (9s +s)* 4

2000 = 10s * 4 = 40s

 

s = 50

 

The wind is 50 mph.

The plane is 450 mph.

 

With the wind:  2000 / (450 + 50) = 2000 / 500 = 4 hours

Against the wind: 2000 / (450 -50) = 2000 / 400 = 5 hours