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.

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

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