SOLUTION: When a plane flies with the​ wind, it can travel 1680 miles in 4 hours. When the plane flies in the opposite​ direction, against the​ wind, it takes 5 hours to fly the same

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Question 1192916: When a plane flies with the​ wind, it can travel 1680 miles in 4 hours. When the plane flies in the opposite​ direction, against the​ wind, it takes 5 hours to fly the same distance. Find the rate of the plane in still air and the rate of the wind.

The rate of the wind is ____ miles per hour.
Found 2 solutions by Alan3354, Edwin McCravy:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
When a plane flies with the​ wind, it can travel 1680 miles in 4 hours. When the plane flies in the opposite​ direction, against the​ wind, it takes 5 hours to fly the same distance. Find the rate of the plane in still air and the rate of the wind.

The rate of the wind is ____ miles per hour.
==========================================
Find the 2 groundspeeds, downwind and upwind.
The plane's airspeed is the average of the 2.
========
Windspeed = difference between airspeed and groundspeed.
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
Make this chart. Let r = rate in still air, and
let w = the rate of the wind.

              | Rate | Time | Distance
-----------------------------------------         
With the wind | r+w  |   4  |  1680
-----------------------------------------
Against wind  | r-w  |   5  |  1680 


               Rate  x Time = Distance 

                   (r+w)(4) = 1680 
                   (r-w)(5) = 1680

                

                Divide the first through by 4 and the
                second through by 5:

                 

Add those two equations term by term, and the w's will cancel
and you can find r.  Then substitute to find w.

Edwin
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