SOLUTION: A plane flies 720 mi. against a steady 30-mi/hr headwind and then returns to the same point with the wind. If the entire trip took 10hrs, what is the planes speed in still air?

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Question 57055: A plane flies 720 mi. against a steady 30-mi/hr headwind and then returns to the same point with the wind. If the entire trip took 10hrs, what is the planes speed in still air?
Answer by Scriptor(36) (Show Source):
You can put this solution on YOUR website!
Hello,
This question is not as innocent as it looks :-)
First thing to know:
SPEED * TIME = DISTANCE

Call T the time to get to the point at 720 miles.
Call t the time to get back at the starting point.
We know that T + t = 10
Call x the speed of the plane. We need to know x.
Using speed*time = distance we obtain:
(x-30)T + (x+30)t = 1440
Replace T by 10 -t and work it out to obtain:
x + 6t = 174
But: we also know that the distance is 720 (for a one way ticket :-) )
Thus: (x + 30)t = 720
Replace x by 174 - 6t to obtain:
-6t� + 204t - 720 = 0
Solve this for t. Hint: D = 156�
You get 2 solution: t= 4 and t=30
t = 30 is false because the time < 10
We now know that t = 4 and thus T = 6
Since (x + 30)t = 720 => (x+30)*4 = 720
x = 150
Greets,
Scriptor