Question 428014
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A plane flies 435 miles with the wind and 345 miles against the wind in the same length of time. 
If the speed of the wind is 15 mph, find the speed of the plane in still air.
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        The solution in the post by @manath is incorrect.

        I came to bring a correct solution.



<pre>
let speed in still air be x mph
wind speed 15 mph  (given).

..

against wind x - 15 mph
with    wind x + 15 mph


Distance against   wind 345
Distance with tail wind 435


    Write the "time" equation



345 /(x- 15) = 435 /(x+15)    (1)

345 *(x+ 15) = 435 *(x- 15)

345 x + 345*15 = 435 x - 435*15

345*15 + 435*15 = 435x - 345x

11700 = 90x

x = 11700/90 = 130 mph.


<U>ANSWER</U>.  The speed of the plane in still air is 130 mph.


<U>CHECK</U>.  Let's check time (equation (1)):  345/115 = 3 hours;  435/145 = 3 hours.  ! correct !
</pre>

Solved correctly.