Question

Dave and Sandy Hartranft are frequent flyers with a particular airline. They often fly from City A to City​ B, a distance of 792792 miles. On one particular​ trip, they fly into the​ wind, and the flight takes 22 hours. The return​ trip, with the wind behind​ them, only takes 1 and one half1 1 2 hours. If the wind speed is the same on each​ trip, find the speed of the wind and find the speed of the plane in still air.

Answer 1

Answer: the speed of the wind is 66 mph and the speed of the plane in still air is 462 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 distance between city A and city B is 792 miles.

On one particular​ trip, they fly into the​ wind, and the flight takes 2 hours. This means that the total speed at which they flew is (x - y) mph.

Distance = speed × time

Distance travelled against the wind is expressed as

792 = 2(x - y)

Dividing through by 2, it becomes

396 = x - y- - - - - - - -1

The return​ trip with the wind behind​ them, it took 1 and one half hours. This means that the total speed at which they flew is (x + y) mph. Distance travelled with the wind is expressed as

792 = 1.5(x + y)

Dividing through by 1.5, it becomes

528 = x + y- - - - - - - - - - -2

Adding equation 1 to equation 2, it becomes

924 = 2x

x = 924/2

x = 462 mph

Substituting x = 462 into equation 2, it becomes

528 = 462 + y

y = 528 - 462

y = 66 mph