# Jay flew his airplane 500km against the wind in the same time that it took him to to fly it 600km with the wind. The speed of the wind was 20km/h. What was the average speed of the airplane? Suppose x is the speed of the airplane.

We also need to know that d=rt so `t=d/r`

So the rate with the wind is x+20, and the rate against is x-20 so using the above formula for time we have

` 600/(x+20)=500/(x-20)`   cross multiplying we get

600(x-20) = 500(x+20)   distributing

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Suppose x is the speed of the airplane.

We also need to know that d=rt so `t=d/r`

So the rate with the wind is x+20, and the rate against is x-20 so using the above formula for time we have

` 600/(x+20)=500/(x-20)`   cross multiplying we get

600(x-20) = 500(x+20)   distributing

600x - 12000 = 500x + 10000   Subtracting 500x and adding 12000 gives us

100x = 22000   solving for x

x = 220km/hr    our answer, which is a reasonable rate for a plane.

We could check,

time with the wind = 600/(220+20) = 600/240 = 2.5 hours

time against the wind = 500/(220-20) = 500/200 = 2.5 hours