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A jet liner flying east with the wind traveled 4200 km in 7 hours.
The return trip, flying against the wind, took 10 hours.
Find the rate at which the jet flew in still air and the rate of the wind.
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From the condition you have these two equations
= u + v, (1)
= u - v. (2)
The left side of the equation (1) is the speed of the plane relative the ground when flying with the wind,
and it is the sum of the rate of the plane in still air "u" and the wind's rate "v".
The left side of the equation (2) is the speed of the plane relative the ground when flying against the wind,
and it is the difference of the rate of the plane in still air "u" and the wind's rate "v".
Simplify the equations (1) and (2):
u + v = 600, (3)
u - v = 420 (4)
Now add the equations (3) and (4). You will get
2u = 600 + 420 = 1020, or u = 1020/2 = 510.
Thus you just found the speed of the plane in still air. It is 510 miles per hour.
Now it is easy to find the speed of the wind. It is
v = 600 - 510 = 90 miles per hour.
ANSWER. The speed of the plane in still air is 510 mph. The speed of wind is 90 mph.
Solved.