Question

A plane traveled 1012 miles each way to Warsaw and back. The trip there was with wind. It took 11 hours. The trip back was into wind. The trip back took 22 hours. What is the speed of the plane in still air? What is the speed of the wind?

Answer 1

Answer: speed of plane is 69/miles per hour

Speed of wind is 23 miles per hour

Step-by-step explanation:

Let x represent the speed of the plane.

Let y represent the speed of the wind.

A plane traveled 1012 miles each way to Warsaw and back. The trip there was with wind. It took 11 hours.

This means that the speed is x+y miles/hour. Therefore

1012 = 11(x+y)

1012 = 11x + 11y - - - - - - - - 1

The trip back was into wind. The trip back took 22 hours.

Since it flew against the wind, the speed would be x-y km/hour

Distance = speed × time. Therefore

1012 = 22(x - y )

1012 = 22x - 22y

Dividing through by 2

506 = 11x - 11y- - - - - - - - - 2

Adding equation 1 and equation 2, it becomes

1518 = 22x

x = 1518/22 = 69

Substituting x = 69 into

1012 = 22(x - y )

x - y = 1012/622= 46

y = 69 - 46 = 23