Answer: A. Wind is 29 mph
Explanation:
We can define:
Sp = speed of the plane
Sw = speed of the wind.
When the plane travels in the same direction that the wind flows, we can write the total speed as:
S = Sp + Sw
And when the plane travels against the flow of the wind, we can write:
S = Sp - Sw.
Now, we have the relation:
Distance = Speed*Time.
We know that:
Distance = 696 mi.
"The trip there was with the wind. It took 6 hours. "
then:
696mi = (Sp + Sw)*6h
"The trip back was into the wind. The trip back took 12 hours."
696mi = (Sp - Sw)*12h.
Then we have the system of equations:
696mi = (Sp + Sw)*6h
696mi = (Sp - Sw)*12h.
First, let's isolate one of the variables in one of the equations, i will isolate Sp in the first eq:
696mi/6h = Sp + Sw
116 mph - Sw = Sp.
Now we can replace this into the other equation:
696mi = (116mph - Sw - Sw)*12h
Let's solve this for Sw, that is the value that we want to find:
696mi/12h = (116mph - 2*Sw)
58mph - 116mph = -2*Sw
-58mph/-2 = Sw = 29mph.
The correct option is A.