A plan traveled 324 miles each way to Austin and back. The trip there was with the wind. It took 3 hours. The trip back was into the wind. The trip took 6 hours. Find the speed of the plan in still sir and the speed of the wind.

the speed of the plane in still air is 81 mph.

the speed of the wind is 27 mph.

Step-by-step explanation:

Let x represent the speed of the plane in still air.

Let y represent the speed of the wind.

The trip there was with the wind. It means that total speed at which the plane travelled with the wind is

(x + y) mph.

It took 3 hours and the distance travelled was 324 miles.

Distance = speed × time

Distance travelled with the wind is

324 = 3(x + y)

Dividing both sides of the equation by 3, it becomes

108 = x + y-- - - - - - - - -1

The trip back was into the wind. It means that total speed at which the plane travelled into the wind is

(x - y) mph.

It took 6 hours and the distance travelled was also 324 miles.

Distance travelled into the wind is

324 = 6(x - y)

Dividing both sides of the equation by 6, it becomes

54 = x - y-- - - - - - - - -2

Adding equation 1 to equation 2, it becomes

162 = 2x

x = 162/2

x = 81

Substituting x = 81 into equation 1, it becomes

108 = 81 + y

y = 108 - 81

y = 27

idn

step-by-step explanation: