SOLUTION: a rescue helicopter is flying from an aircraft carrier 350 mi to peral harbor hospital. the point of no return is the point here it would take as much time to fly back to the airc

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Question 221986: a rescue helicopter is flying from an aircraft carrier 350 mi to peral harbor hospital. the point of no return is the point here it would take as much time to fly back to the aircraft carrier as it would to fly on to pearl harbor. the airspeed of the helicopter is 175 mi/h and it is flying into a 25 mi/h headwind.
a. calculate the total time for the helicopter to fly to pearl harbor
b. once the helicopter is at the point of no return, determine the time it will take to complete the trip.
c. use the results from part a and b to determine the time for the helicopter to reach the point of no return.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
a rescue helicopter is flying from an aircraft carrier 350 mi to Pearl harbor hospital.
The point of no return is the point where it would take as much time to fly back
to the aircraft carrier as it would to fly on to pearl harbor.
The airspeed of the helicopter is 175 mi/h and it is flying into a 25 mi/h headwind.
a. calculate the total time for the helicopter to fly to pearl harbor
t = 350%2F%28%28175-25%29%29
t = 350%2F%28%28150%29%29
t = 21%2F3 hrs (2 hrs 20 min)
:
b. once the helicopter is at the point of no return, determine the time it will take to complete the trip.
:
Let p = point of no return (miles from carrier)
Then (350-p) = miles from Pearl Harbor
:
return to carrier = continue to Pearl
p%2F%28175%2B25%29 = %28350-p%29%2F%28175-25%29
p%2F%28200%29 = %28350-p%29%2F%28150%29
Cross multiply
150p = 200(350-p)
150p = 70000 - 200p
150p + 200p = 70000
350p = 70000
p = 70000%2F350
p = 200 mi from carrier is point of no return. (150 mi from Pearl)
:
c. use the results from part a and b to determine the time for the helicopter to reach the point of no return.
t = 200%2F%28175-25%29
t = 200%2F%28150%29
t = 11%2F3 hrs
:
:
This checks out, it would take 1 hr to cover the remaining 150 mi at 150 mph
1 + 11%2F3 = 21%2F3 as found in part a
and
to return to the carrier, with the wind, 200 mi at 200 mph = 1 hr also