Question 1025411
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Flying against the wind, an airplane travels 3800km in 5 hours. 
Flying with the wind, the same plane travels 3660km in 3 hours. 
What is the rate of the plane in still air and what is the rate of the wind?
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<pre>
Let u be the rate of the plane at no wind (in kilometers per hour)
and v be the rate of the wind (in the same units).


Then the effective rate  of the plane with   the wind is u + v
and  the effective rate of the plane against the wind is u - v.


From the problem, the effective rate of the plane against the wind is the distance of 3800 kilometers 
divided by the time of 5 hours  {{3800/5}}} = 760 km/h.


                  The effective rate of the plane with the wind is the distance of 3660 kilometers 
divided by the time of 3 hours  {{{3660/3}}} = 1220 mph.


So, we have two equations to find 'u' and 'v'

    u + v = 1220,    (1)

    u - v =  760.    (2)


To solve, add equations (1) and (2).  The terms 'v' and '-v' will cancel each other, and you will get

    2u = 1220 + 760 = 1980  --->   u = 1980/2 = 990.

Now from equation (1)

     v = 1220 - 990 = 280 - 220 = 230.


<U>ANSWER</U>.  The rate of the plane in still air is 990 km/h.  The rate of the wind is 230 km/h.
</pre>

Solved.