This is a wind velocity problem A plane can fly 340 miles pe

This is a wind velocity problem. A plane can fly 340 miles per hour in still air. If it can fly 200 miles downwind in the same amount of time it can fly 140 miles upwind, find the velocity of the wind.

Solution

Let w = the velocity of the wind, and t = the time. When the jet is flying downwind, it is flying in the same direction as the wind, so it flys faster than the still airspeed. When it is flying upwind, it is flying in the opposite direction from the wind (against the wind), so in this case the wind slows down the plane. In table format, this is:

__Formula: ( Rate ) x (Time)= (Distance)
Downwind: (340 + w) x ( t ) = ( 200 )
__Upwind: (340 - w) x ( t ) = ( 140 )

To solve, notice that the times are the same. Rewrite the distance equation to solve for \"t\":
t = d / r
t = 200 / (340 + w)
t = 140 / (340 - w)

Now set the two equations (above) equal to each other and solve for w:

200 / (340 + w) = 140 / (340 - w)
200 (340 - w) = 140 (340 + w)
68000 - 200w = 47600 + 140w
20400 = 340w
w = 60 mph

To check your work, calculate the time for the downwind and upwind conditions:

Downwind time = 200 / (340 + 60) = 0.5 hours
Upwind time = 140 / (340 - 60) = 0.5 hours