SOLUTION: A plane is flying the 3,458 mile trip from New York City to London has a 50 MPH tailwind. The flight's Point of No Return is the point at which the flight time required to return t

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Question 141347: A plane is flying the 3,458 mile trip from New York City to London has a 50 MPH tailwind. The flight's Point of No Return is the point at which the flight time required to return to New York is the same a the time required to continue to London. If the speed on the plane in still air is 360 MPH, how far is New York from the point of no return?
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A plane is flying the 3,458 mile trip from New York City to London has a 50 MPH tailwind. The flight's Point of No Return is the point at which the flight time required to return to New York is the same a the time required to continue to London. If the speed on the plane in still air is 360 MPH, how far is New York from the point of no return?
:
From the given information we can say:
360 + 50 = 410 mph speed (relative to the earth) with the wind
360 - 50 - 310 mph speed against the wind
:
Let d = dist to New York from point of no return
Then
(3458-d) = dist to London from point of no return
:
Write a time equation: Time = dist/speed
:
Return to N.Y time = Continue to London time
d%2F310 = %28%283458-d%29%29%2F410
Cross multiply:
410d = 310(3458-d)
:
410d = 1071980 - 310d
:
410d + 310d = 1071980
:
720d = 1071980
d = 1071980%2F720
d = 1488.86 mi from N.Y.
:
:
Check solution by finding the distance to London and calculating the time to both:
3458 - 1488.86 = 1969.14 mi to London
:
Time to N.Y.: 1488.86/310 = 4.8 hrs
Time to Lond: 1969.14/410 = 4.8 hrs