Given:
a.) A jet travels 4,634 miles against the wind in 7 hours.
b.) It also travels 5,334 miles with the wind in the same amount of time.
Distance = Rate x Time
Let,
J = rate of jet in still air
W = rate of wind
Then the jet travels at (J - W) against the wind and (J + W) with the wind so,
4,634 = (J - W) x 7
4,634 = 7J - 7W (against the wind)
5,334 = (J + W) x 7
5,334 = 7J + 7W (with the wind)
Add these equations together to conveniently cancel the W's to get,
Total Distance = Total Travel Time x Rate of Jet in still air
4,634 + 5,334 = 14 x J
9,968 = 14J
14J/14 = 9,968/14
J = 712
Plug this value for J into the 1st equation and solve for W,
4,634 = 7J - 7W
4,634 = 7(712) - 7W
4634 = 4984 - 7W
-7W = 4634 - 4984
-7W = -350
-7W/-7 = -350/-7
W = 50
So the rate of the jet in still air is 712 mph and the rate of the wind is 50 mph.