Solving a distance, rate, time problem using a system of linear equations

Question

Flying against the jetstream, a jet travels 4400

miles in 8

hours. Flying with the jetstream, the same jet travels 3640

miles in 4

hours. What is the rate of the jet in still air and what is the rate of the jetstream?

Answer 1

If we let X = speed of jet and Y = jet-stream speed:

8(x-y) = 4400

4(x+y) = 3640

If we simplify these equations:

x-y = 550

x+y = 910

Taking a step back, the simplified equations make sense. If both speeds are going in the same direction, then their combined result will be more positive then when the speeds are going against each other.

Combing the equations, we get:

x - y = 550

x + y = 910 (Solve for x)

2x = 1460

x = 730 miles per hour

Solve for y using first equation:

730 - y = 550

730 = 550 + y

180 miles per hour = y