Question

When a plane flies into the wind, it can travel 3000 miles in 6 hours. When it flies with the wind, it can travel the same distance in 5 hours. Find the rate of the plane in still air and the rate of the wind

Answer 1

Answer: the rate of the plane in still air is 550 mph and the rate of the wind is 50 mph

Step-by-step explanation:

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

Let y represent the rate of the wind.

When a plane flies into the wind, it can travel 3000 miles in 6 hours. The total speed with which the plane flew is x - y

Distance = speed × time

Therefore,

3000 = 6(x - y)

Dividing through by 6, it becomes

500 = x - y - - - - - - - - - - - - - -1

When it flies with the wind, it can travel the same distance in 5 hours.

The total speed with which the plane flew is x + y

Distance = speed × time

Therefore,

3000 = 5(x + y)

Dividing through by 5, it becomes

600 = x + y - - - - - - - - - - - - - -2

Adding equation 1 to equation 2, it becomes

1100 = 2x

x = 1100/2 = 550

Substituting x = 550 into equation 1, it becomes

500 = 550 - y

y = 550 - 500

y = 50