A plane flies 720 mi against a steady 30 mih headwind and th

A plane flies 720 mi against a steady 30 mi/h headwind and then returns to the same point with the wind. If the entire trip takes 10h, what is the plane\'s speed in still air?

Solution

WITH THE WIND DATA:
distance =720 mi ; rate= plane speed +30 ; time =d/r= 720/(p+30)
AGAINST THE WIND DATA:
distance = 720 mi ; rate = plane speed -30; time = d/r = 720/(p-30)
EQUATION:
720/(p+30) + 720/(p-30) = 10
72/(p+30) + 72/(p-30) = 1
72p-72*30+72p+72*30 = (p+30)(p-30)
144p=p^2-900
p^2-144p-900=0
(p-150)(P+6)=0
p=150 mph. ( The plane\'s speed in still air is 150 mph)