Expert: Scott A Wilson - 5/8/2010

Question
If a plane can fly with the wind 3360 miles in 7 hours and make the return flight against the wind in 8 hours, what is the speed of the pane in calm air?

I'm doing a test review but the teacher didn't go through this problem during the review and I already have the answer but would it be possible to show me the steps of solving it. Thanks in advance.

Answer
It is known that d = rt, where d = distance, r = rate, and t = time.
We know that distance is 3360.

We know the time with the winds takes 7 hours.
We know the time against the wind takes 8 hours.

This makes the speed with the wind into 3360/7 = 480.
This makes the speed against the wind into 3360/8 = 420.

To find the speed of the airplance in calm air, take the average of those two.
See, if the plane flies at speed x and the wind is at y, we know
x+y=480 and x-y=420, so y must be the number halfway between 420 and 480.