SOLUTION: An airplane flies 72 miles with a 30-mph tailwind and then flies back into the 30-mph wind. If the time for the round trip was 1 hour, find the speed of the airplane in calm air.

 

Hi,

An airplane, with speed in calm air , flies 72 miles with a 30-mph tailwind and then flies back into the 30-mph wind...

round trip was 1 hour

Note D = rt OR D/r = t

    |Multiplying thru by (r+30)(r-30) so as all denominators = 1

   72(r-30) + 72(r+30) =  (r+30)(r-30) 

         144r = r^2 - 900

    r^2 - 144r -900 = 0

factoring

(r -150)(r+6) = 0

    r = 150mph   (throwing out the negative solution for speed)

   150mph was the airplane speed in calm air

CHECKING our Answer***

72/180 + 72/120 =  = 1