When a small plane flies with the wind, it can travel 800 miles in 5 hours. When the plane flies in the opposite direction, against the wind, it takes 8 hours to fly the same distance. What is the rate of the plane in still air and the rate of the wind?

1 Answer
Parabola
Nov 26, 2017

The plane will travel 130mph in still air and the wind current is 30mph.

Explanation:

First, let #x# be the speed of the plane when travelling in still air and #y# the speed of wind. When the plane is travelling against the wind, the speed is #x-y#. When it is going with the wind, the speed is #x+y#.

Using the formula #d=rt# you could write the following equations.

#5(x+y)=800#
#8(x-y)=800#

Simplify to get
#x+y=160#
#x-y=100#

Subtract both equations to get
#2y=60#

Therefore, #y# is 30. Plug in the value to one of the equations to get the value of #x#. #x# is 130. You now have the answer!

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