Problema Solution
Working together, Bill and Tom painted a fence in 4 hours. Last year, Tom painted the fence by himself. The year before, Bill painted it by himself, but took 6 hours less than Tom took. How long did Bill and Tom take, when each was painting alone?
Answer provided by our tutors
Define:
4(b + 6) + 4(b) = (b)(b + 6)
4b + 24 + 4b = b2 + 6b
8b + 24 = b2 + 6b
0 = b2 - 2b - 24
(b - 6)(b + 4) = 0
Then, since b = 6, then Bill takes 6 hours. Tom takes 6 hours longer than Bill, so:
Bill takes 6 hours, and Tom takes 12 hours.