Question

A plane can fly 260 miles downwind in the same amount of time as it can travel 170 miles upwind. Find the velocity of the wind if the plane can fly 215 mph in still air.

Answer 1

From the two statements we can say:

260=(215+w)t

t=260/(215+w)

Now from the second statement:

170=(215-w)t

t=170/(215-w)

We are told that t=t, for the downwind and upwind equations so:

260/(215+w)=170/(215-w)

260(215-w)=170(215+w)

55900-260w=36550+170w

-430w=-19350

w=45

So the wind speed is 45mph.