Question

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.

Answer 1

Answer: 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