SOLUTION: A plane flying the​ 3458-mi from New York City to London has a 70 ​-mph tailwind. The​ flight's point of no return is the point at which the flight time requir

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Question 1056202: A plane flying the​ 3458-mi from New York City to London has a 70
​-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 as the time required to continue to London. If the​ plane's speed in still air is 900

​mph, how far is New York from the point of no​ return?
Found 3 solutions by josmiceli, Boreal, Alan3354:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = distance from point of no return to NYC
+3458+-+d+ = distance from point of no return to London
Let +t+ = time in hrs to fly from point of no return
back to NYC and also the time in hrs to London
--------------------------------------------------------
Equation for point of no return back to NYC
(1) +d+=+%28+900+-+70+%29%2At+
Equation for point of no return to London
(2) +3458+-+d+=+%28+900+%2B+70+%29%2At+
-------------------------------------------------
Note that you have to keep track of the wind direction.
Substitute (1) into (2)
(2) +3458+-+%28+900+-+70+%29%2At+=+%28+900+%2B+70+%29%2At+
(2) +3458+-+900t+%2B+70t+=+900t+%2B+70t+
(2) +1800t+=+3458+
(2) +t+=+1.921+ hrs
This is 1 hr 55 min 16 sec
-----------------------------
Check:
(1) +d+=+%28+900+-+70+%29%2At+
(1) +d+=+830t+
(1) +d+=+830%2A1.921+
(1) +d+=+1594.43+
and
(2) +3458+-+d+=+%28+900+%2B+70+%29%2At+
(2) +3458+-+d+=+970t+
(2) +d+=+3458+-+970t+
(2) +d+=+3458+-+970%2A1.921+
(2) +d+=+3458+-+1863.37+
(2) +d+=+1594.63+
Close enough, I think -OK

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
speed*time=distance
The distance the plane is from NY is 970 mph*time in hours, going east
At any given point, the time required to go to London is distance/speed
The time required to go back to NY is distance/speed
To London, we will call the distance x
To New York, we will call the distance 3458-x
speed to London is 970 mph
speed to New York is 830 mph
Time to London is x/970
Time to NY is (3458-x)/830
They are equal.
(3458-x)/830=x/970
Cross-multiply
3354260-970x=830x
1800x=3354260
x=1863.48 miles
The distance to New York requires an extra step since I didn't make the distance x.
1594.52 miles ANSWER
at 970 mph, 1863.48 miles is 1.921 hours
at 830 mph 1594.52 miles is 1.921 hours

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Planes use knots, not mi/hr.