Aplane is traveling 600 miles. it takes the plane 5 hours against the wind and 4 hours with the wind. what is the speed of the plane in still air, and what is the speed of the wind?

the speed of the plane in still air is 135 miles per hour

the speed of the wind is 15 miles per hour

Step-by-step explanation:

Let x represent the speed of the plane in still air

Let y represent the speed of the wind.

The distance travelled by the plane is 600 miles.

Distance travelled = speed × time

It takes the plane 5 hours against the wind. This means that the total speed is (x-y) miles per hour. Therefore,

600 = 5(x- y) = 5x - 5y - - - - - - - 1

It takes the plane 4 hours with the wind. This means that the total speed is (x+y) miles per hour. Therefore,

600 = 4(x+ y) = 4x + 4y - - - - - - - - 2

Multiplying equation 1 by 4 and equation 2 by 5, it becomes

2400 = 20x - 20y

3000 = 20x + 20y

Adding both equations

5400 = 40x

x = 5400/40 = 135

Substituting x = 135 into equation 1, it becomes

4 × 135 + 4y = 600

540 + 4y = 600

4y = 600 - 540 = 60

y = 60/4 = 15

2nd one in the first row is correct