a plane flying with the jet stream flew from los angeles to

a plane flying with the jet stream flew from los angeles to chicago, a distance of 2250 mi, in 5 h. flying aganst the jet stream, the plane couldfly only 1750 mi in the same amount of time. find the rate of the plane in calm air and the rate of wind.

Solution

Let x = speed of plane in still air
Let y = speed of the jet stream
Then:
(x+y) = speed with the jetstream
(x-y) = speed against the jetstream
:
Write two distance equations: Distance = time * speed
5(x + y) = 2250
5(x - y) = 1750
:
Simplify both equations, divide by 5
x + y = 450
x - y = 350
------------- adding eliminates y
2x + 0 = 800
x = 800/2
x = 400 mph in still air
:
Find y using x + y = 800
400 + y = 450
y = 50 mph speed of the jet stream
:
:
Check solutions by finding the distance at both speeds:
5*450 = 2250
5*350 = 1750