A plane flies 720 miles against a steady 30 mile per hour he

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

Solution

Let \"p\" be plane speed without wind.

With the wind DATA:
distance=720 mi ; rate= p+30 mph ; time = d/r = 720/(p+30) hr.

Against the wind DATA:
distance=720 mi ; rate = p-30 mph ; time =d/r = 720(p-30) hr.

EQUATION:
time + time = 10 hrs
720/(p+30) + 720/(p-30) = 10
72/(p+30) + 72/(p-30) = 1
72p + 72p = 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)