Answer: 20 mph
Explanation:
Speed is a physical quantity which is equal to the ratio between the distance covered (d) and the time taken (t):
\(v=\frac{d}{t}\)
In the first part of the problem, the plane flew a distance of d=400 mi in a time of t=2.5 h. The speed of the plane in this case was the difference between the proper speed of the plane, v, and the speed of the wind, w, since the plane flew opposite to the wind. So we can write:
\(v-w=\frac{400mi}{2.5h}=160 mph\) (1)
During the return trip, the plane flew with a speed (v+w), since the wind was on the tail, and it took 2 hours to cover the same distance:
\(v+w=\frac{400 mi}{2 h}=200 mph\) (2)
So we have two equations with two unknown variables. From (1), we get
\(v=160+w\)
Substituting into eq.(2)
\((160+w)+w=200\\160+2w=200\\2w=40\\w=20 mph\)
So, the speed of the wind was 20 mph.
