A plane traveled 696 miles each way to New York City and back. The trip there was with the wind. It took 6 hours. The trip back was into the wind. The trip back took 12 hours. What is the speed of the wind? A. Wind is 29 mph
B. Wind is 87 mph
C. Wind is 46 mph
D. Wind is 15 mph

A. Wind is 29 mph

Step-by-step 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.