Problema Solution
Against the wind a small plane flew 245 miles in one hour and 10 minutes. The return trip took only 50 minutes. What was the speed of the wind? What was the speed of the plane in still air?
Answer provided by our tutors
x = rate of the wind
v = speed of the small plane in still air
1 hour and 10 min = 1 10/60 hours = 7/6 hours
the speed of the plane against the wind is v - x = 245 / (7/6) miles per hour
the return trip flying in the direction of the wind with speed v + x took 50 min = 50/60 = 5/6 hours
thus we can write
v - x = 245 / (7/6)
v + x = 245/ (5/6)
by solving the system of equations
v = 262 mph
x = 82 mph
The speed of the plane in still air is 262 mph.
The speed of the wind is 82 mph.