Question 1179658
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A plane traveling with the wind flew 1312.5 mi in 5.25 h. 
Against the wind, the plane required 6.25 h to fly the same distance. 
Find the rate of the plane in calm air and the rate of the wind.
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Let x be the rate of the plane in calm air, in miles per hour.

Let y be the rate of the wind.


Then  the effective speed of the plane with    the wind is (x+y) mph,

while the effective speed of the plane against the wind is (x-y) mph,



From the problem, the effective rate of the plane with the wind is  the distance divided by the travel time

    {{{1312.5/5.25}}} = 250 miles per hour,


and the effective rate of the plane against the wind is  the distance divided by the travel time

    {{{1312.5/6.25}}} = 210 miles per hour.


So, we have these two equations

    x + y = 250     (1)

    x - y = 210     (2)


To find x, add the equation.  You will get

    2x = 250 + 210 = 460,  x = 460/2 = 230.


Now express y from equation (1) and calculate

    y = 250 - x = 250 - 230 = 20.


At this point the problem is solved completely.


<U>ANSWER</U>.  The speed of the plane in calm air is 230 mph.  The rate of the wind is 20 mph.
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Solved.