Question

A plane traveled 400 miles to Rome and back. The trip there was with the wind. It took 5 hours. The trip back was into the wind. The trip back took 10 hours.
- Find the speed of the plane in still air and the speed of the wind.

Answer 1

Assuming that each way is 400 miles, (even though in Rome they wouldn't know what miles are, and would be using km.)

let speed of plane in still air be x mph
let speed of wind be y mph

going with the wind:
5(x+y) = 400 ---> x + y = 80
going against the wind:
10(x-y) = 400 ---> x - y = 40

add them:
2x = 120
x = 60
then y = 20

the speed of the plane is 60 mph, and the wind has a speed of 20 mph.
(that's a pretty slow plane)

Answer 2

how did you get y=20