# Math

posted by .

Use systems of lineear equations to solve:

An airplane flew for 6 hours with a 22-km/h tail wind. The return flight against the same wind took 8 hours. Find the speed of the plane in still air.

I know the answer is 154 km/hr (back of book resources :) )...I just don't understand how you would get to that answer.

• Math -

Use the equation d = rt, once for each trip. I will use capitals for the variables and lowercase for subscripts.

D = R * T
Dr = Rr * Tr

where "r" is a subscript used to indicate that values for the return tripe.

We are given the time for each trip: 6 hours and then 8 hours for the return trip.

D = R * 6
Dr = Rr * 8

And the rate for both trips is based on x -- the speed in still air. It is x + 22 in one direction and x - 22 in the other.

D = (x + 22) * 6
Dr = (x - 22) * 8

Finally, we know that the distance is the same for both trips.

D = Dr

Therefore, through transitibity, we know that the right sides of both of equations are equal.

(x + 22) * 6 = (x - 22) * 8

or

6(x + 22) = 8(x - 22)

Solve that and you will get 154.