Answer:
speed of the wind, w = 20 mph
Step-by-step explanation:
Let,
s = speed in still air = 120 mph
w = wind speed = ?
t = travel time in hours
Plane traveling with the wind, we have:
(v + w)t = 700
(120 + w)t = 700 ------------------(equation 1)
Plane traveling against the wind, we have:
(v - w)t = 500
(120 - w)t = 500 --------------------(equation 2)
From equation 1, make t subject of formula,
t = 700/(120 + w) -------------------(equation 3)
From equation 2, make t also subject of formula,
t = 500/(120 - w) ---------------------(equation 4)
It is the same t in both equations, so equating equation 3 and 4
700/(120 + w) = 500/(120 - w)
Solve for w.
500(120 + w) = 700(120 - w)
60000 + 500w = 84000 - 700w
500w + 700w = 84000 - 60000
1200w = 24000
w = 24000/1200
w = 20 mph
