this is for my homework.

Question

An airplane travels 1372 kilometers against the wind in 2 hours and 1552 kilometers with the wind in the same amount of time. What is the rate of the plane in still air and what is the rate of the wind?

Answer 1

1372 km against the wind

1552 with the wind

d=rt, distance = rate of speed times time, t= d/r, t=2

let p = speed of plane in still air, w = speed of the wind

2=1372/(p-w)

2p-2w -1372, p-w= 686,

p = 686+w

2 = 1372/(p-w) = 1552/(p+w)

1372(p+w) = 1552(p-w)

1372p + 1372w = 1552p - 1552w

(1552-1372)p = (1552+1372)w

180p = 2924w

180(686+w) = 2924w

2924w-180w = 180(686)

w = 180(686)/2744 = 45km/hr = wind speed

p = 686+45 = 731 km per hr= plane speed in still air

Answer 2

Against the wind, the wind works against the speed. With the wind, the wind aids the speed.

2(p - w) = 1372

2(p + w) = 1552

p - w = 686

p + w = 776

2p = 1462

p = 731 mph

731 + w = 776

w = 45 mph