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Challenging Algebra Question?

Suppose you are flying an ultralight aircraft like the one pictured at the left. You are flying to a nearby town, 18 miles away. With a tail wind, the trip takes 1/3 hour. Your return flight with a head wind talkes 3/5 hour.
a. Find the average airspeed of the ultralight aircraft.
b. find the average wind speed.

Let the plane speed be P. Let the wind speed be W.
So (P+W) * 1/3 = 18 ... (1)
And (P-W) * 3/5 = 18 ... (2)
Multiple (1) by 9 and (2) by 5.
3P + 3W = 162 ... (3)
3P - 3W = 90 ... (4)
Adding (3) and (4) gives:
6P = 252
So P = 42miles per hour.
Sub that back into (3) gives:
3*42 + 3W = 162
126 + 3W = 162
3W = 36
W = 6 miles per hour.

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