SOLUTION: A pilot flies 1050 mi with a tailwind of 20mph. Against the wind, he flies only 850 mi in the same amount of time. What is the speed of the plane in still air?

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Question 1142254: A pilot flies 1050 mi with a tailwind of 20mph. Against the wind, he flies only 850 mi in the same amount of time. What is the speed of the plane in still air?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.
If x is the speed of the plane at no wind (in miles per hour), then

    the effective ground speed with the wind is (x+20) mph, while 

    the effective ground speed against the wind is (x-20) mph.


The "time" equation then is


    1050%2F%28x%2B20%29 = 850%2F%28x-20%29,


according to the condition   (same amount of time for each flight).


To solve it, cross multiply and simplify


    1050*(x-20) = 850*(x+20)

    1050x - 1050*20 = 850x + 850*20

    1050x - 850x = 850*20 + 1050*20

    x = %28850%2A20+%2B+1050%2A20%29%2F%281050-850%29 = 190.


ANSWER.  The speed of the plane at no wind is 190 miles per hour.


CHECK.   1050%2F%28190%2B20%29 = 1050%2F210 = 5 hours;   850%2F%28190-20%29 = 850%2F170 = 5 hours.    ! Correct !

Solved.

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The lesson to learn from this solution and the things to memorize are : 

    1.  The effective speed of a plane flying with    a wind is the sum        of the two speeds.

    2.  The effective speed of a plane flying against a wind is the difference of the two speeds.

    3.  It gives you a "time" equation, which you easily can solve and find the unknown plane' speed.


Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Time is distance divided by rate.

Since the times with and against the wind are the same, time is also the DIFFERENCE in distances divided by the DIFFERENCE in rates.

The difference in the two rates is twice the wind speed (because the wind speed adds to the speed in one direction and subtracts from it in the other direction).

So the difference in rates is 40mph; the difference in distances is 200 miles. So the time for each flight is 200/40 = 5 hours.

So the speed of the plane with the wind is 1050/5 = 210mph; that makes the speed of the plane in still air 210-20 = 190mph.