Question

I beg of you solve it. A small Plane can travel 120 mph in still air. The plain can fly 700 miles with the wind in the same that it can travel 500 miles against the wind. Find the speed of the wind.
I know the answer is 20 mph based on the book but if u can go near that number then it's find. THANK YOU!

Answer 1

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