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An aircraft flew 2 hours with the wind. The return trip took 3 hours against the wind. If the speed of the plane in still air is 180 miles per hour more than the speed of the​ wind, find the wind speed and the speed of the plane in still air.

 Mar 7, 2020
 #1
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Let  the wind  speed  =  S

Let  the  rate of  the plane in still air = 180  + S

 

So  with  the  wind  the plane's  rate   =  (180 + S + S)  =  (180 + 2S)

Against  the  wind  the plane's  rate = (180 + S  - S) =  (180)

 

And  Time * Rate  = Distance....so......equating distances we have  that

 

2 (180 + 2S) = 3 (180)   simplify

 

360 + 4S  = 540        subtract  360  from both sides

 

4S    =  180      divide  both sides  by  4

 

S =  45  (mph)  =  wind speed

 

180 + S =   180  + 45  =   225 (mph)  =  plane's rate  in still air 

 

 

cool cool cool

 Mar 7, 2020

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