Given:
a.) A plane traveled 264 miles to Carson City and back.
b.) The trip there was with the wind. It took 3 hours.
c.) The trip back was into the wind. The trip back took 6 hours.
Let,
r = rate of the plane, mph.
w = rate of the wind, mph.
The distance to and from Carson City is 264 miles. The time to fly with the wind is 3 hours and the time to return against the wind is 6 hours. Using distance equals the rate multiplied by time, we can write two equations - one for with the wind and one for against the wind, as follows:
(1) (r + w)*3 = 264
(2) (r - w)*6 = 264
or
[(r + w)*3 = 264]/3
(3) r + w = 88
[(r - w)*6 = 264]/6
(4) r - w = 44
Now, let's add equations (3) and (4). We get,
(5) (r + w) + (r - w) = 88 + 44
(6) 2r = 132
2r/2 = 132/2
(7) r = 66 ; speed of the plane
Substitute r = 66 in equation (3) to get w.
r + w = 88
66 + w = 88
w = 88 - 66
(8) w = 22 ; speed of the wind
Therefore, the plane travels at 66 mph and the wind is blowing at 22 mph.