A plane traveled 1100 miles each way to Cairo and back.

Question

The trip there was with the wind. It took 11 hours. The trip back was into the wind. The trip back took 22 hours. Find the speed of the plane in still air and the speed of the wind.

Answer 1

Let p = the speed of the plane in still air and w = the speed of the wind.

My overall speed with the wind is p + w and against the wind is p - w. If I fly 200 mph and the wind is 5 mph, then with the wind I am travelling at 205 mph but upwind I'm travelling 195 mph.

d = rt

1100 = 11(p + w)

1100 = 22(p - w)

100 = p + w

50 = p - w

Adding the 2 equations together...

2p = 150

p = 75 mph

75 - w = 50

w = 25 mph

Answer 2

Set up system of equations:

To Cairo: plane speed + wind speed = 1100 miles / 11 hours = 100 mph

From Cairo: plane speed - wind speed = 1100 miles / 22 hours = 50 mph

Add the system of equations to solve for plane speed:

2 * (plane speed) = 150 mph

plane speed = 150 mph / 2 = 75 mph

Plug plane speed into one of the equations to solve for wind speed:

plane speed + wind speed = 100 mph

wind speed = 100 mph - plane speed = 100 mph - 75 mph = 25 mph

plane speed = 75 mph

wind speed = 25 mph