A plane traveled 1456 miles to Bangkok and back. The trip there was with the wind. It took 13 hours. The trip back was into the wind. The trip back took 26 hours. Find the speed of the plane in still air and the speed of the wind.

speed of the plane in still air is 84 mph; speed of the wind is 28 mph.

Step-by-step explanation:

Let s =speed of plane in still air

let w = speed of the wind

(s+w) = ground speed with wind

(s-w) = ground speed against the wind

Then, use a distance equation for each way. Note that

distance = speed × time

13(s+w) = 1456

26(s-w) = 1456

Divide the 1st equation by 13, and divide the 2nd equation by 26, we will have:

s + w = 112

s - w = 56

Using elimination method

2s = 168

s = 168/2

s = 84

s = 84 mph plane speed in still air

s + w = 112

84 + w = 112

Wind speed, w = 112 - 84 = 28mph