SOLUTION: An air rescue plane averages 300 miles per hour in still air. It carries fuel for 5 hours of flying time. If, upon takeoff, it encounters a head wind of 30 miles per hour, how far

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Question 531211: An air rescue plane averages 300 miles per hour in still air. It carries fuel for 5 hours of flying time. If, upon takeoff, it encounters a head wind of 30 miles per hour, how far can it fly and return safely? (Assume that the wind remains constant)
Found 2 solutions by ankor@dixie-net.com, Alan3354:
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
An air rescue plane averages 300 miles per hour in still air.
It carries fuel for 5 hours of flying time.
If, upon takeoff, it encounters a head wind of 30 miles per hour, how far can it fly and return safely?
(Assume that the wind remains constant)
:
300 - 30 = 270 mph the ground speed against the wind
300 + 30 = 330 mph the ground speed with the wind
:
let d = the one way distance to point of no return
:
Write a time equation, time = dist/speed
:
Outbound time + return time = 5 hrs
+ = 5
multiply by 2970 to get rid of the denominators, results
11d + 9d = 2970(5)
20d = 14850
d =
d = 742.5 mi, but it says "safely", you would never cut it that close; I would say 650 max.
:
:
Confirm this by finding the actual time for each trip
742.5/270 = 2.75 hrs
742.5/330 = 2.25 hrs
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totals time: 5 hrs

Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
An air rescue plane averages 300 miles per hour in still air. It carries fuel for 5 hours of flying time. If, upon takeoff, it encounters a head wind of 30 miles per hour, how far can it fly and return safely? (Assume that the wind remains constant)
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The plane's avg groundspeed for the round trip is
2*330*270/(330 + 270) = 297 mi/hr
Round trip distance = 5*297 = 1485 miles
One way = 742.5 miles