SOLUTION: An airplane flying against the wind travels 165 miles in the same amount of time it would take the same plane to travel 195 miles with the wind. If the wind speed is a constant 30

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Question 743104: An airplane flying against the wind travels 165 miles in the same amount of time it would take the same plane to travel 195 miles with the wind. If the wind speed is a constant 30 miles per hour, how fast would the plane travel in still air?
I think the answer is 180, but my homework says it's incorrect? Why?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
An airplane flying against the wind travels 165 miles in the same amount of time it would take the same plane to travel 195 miles with the wind.
If the wind speed is a constant 30 miles per hour, how fast would the plane travel in still air?
:
Let s = speed in still air
then
(s-30) = ground speed against the wind
and
(s+30) = ground speed with the wind
:
Write a time equation; time = dist/speed
time against = time with
165%2F%28%28s-30%29%29 = 195%2F%28%28s%2B30%29%29
Cross multiply
195(s-30) = 165(s+30)
195s - 5850 = 165s + 4950
195s - 165s = 4950 + 5850
30s = 10800
s = 10800/30
s = 360 mph in still air (you were half right!)
:
:
Confirm this, find the actual time each way, should be equal
165/330 = .5 hrs
195/390 = .5