Problema Solution
The rate of a jet stream is 100 miles per hour. Traveling with the jet stream, an airplane can fly 2400 miles in the same amount of time as it takes to fly 1600 miles against the jet stream. What is the airplanes average rate in calm air?
Answer provided by our tutors
let
x = the airplanes average rate in calm air
s = 100 mph is the rate of a jet stream
t = the amount of time
since rate = distance / time => time = distance/rate
traveling with the jet stream the rate of the airplane will be: x + s = x + 100 mph
in t time it will pass 2400 miles: 2400 = t*(x + 100) => t = 2400/(x + 100)
traveling against the jet stream the rate of the airplane will: x - s = x - 100 mph
in t time it will pass 1600 miles: 1600 = t*(x + 100) => t = 1600/(x - 100)
we can write the equation
2400/(x + 100) = 1600/(x - 100)
and solve it by x
x = 500 mph
the airplanes average rate in calm air is 500 mph.