Question 307439
A jet plane flying with the wind flew 2400 miles in 4 hours. Against the wind, the plane flew only 2000 miles in 4 hours. Find the rate of the plane in calm air and the rate of the wind.


let the the rate of plane instill air be x mph
& the rate of wind be y mph
.

with wind the rate will be x+y mph

Against wind the rate will be x-y mph
.
Time taken with wind will be 2400 / x+y......  ( time = distance / rate)
Time taken against wind will be 2000/ x-y
.

2400 /x+y = 4

2000/ x-y =4

.
4(x+y)=2400
4(x-y)=2000
.

4x+4y=2400
4x-4y=2000
.

Add the two equations
.
4x+4y+4x-4y= 4400

8x= 4400
x= 550 mph the rate of the plane
.
4x+4y=2400
plug the value of x 

4*550+4y= 2400

2200 +4y= 2400
4y= 2400-2200

4y=200

y=50 mph the rate of the wind
.
.

Ananth