SOLUTION: A sink has 2 faucets, A and B, and drain, C. The drain empties the sink at the same rate that faucet A fills the sink. If drain C is closed and both faucets are turned on, the sink

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A sink has 2 faucets, A and B, and drain, C. The drain empties the sink at the same rate that faucet A fills the sink. If drain C is closed and both faucets are turned on, the sink      Log On


   

Question 349502: A sink has 2 faucets, A and B, and drain, C. The drain empties the sink at the same rate that faucet A fills the sink. If drain C is closed and both faucets are turned on, the sink is filled in 5 minutes. If faucet B is on, and drain C is open, the sink is filled in 20 minutes. Find the rates at which faucets A and B fill the sink.
I'm not sure how to set this up. I got 7.5 for A and 12.5 for B.
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
(5/A) + (5/B) = 1 ___ 5B + 5A = AB ___ 5B = AB - 5A ___ 5B = A(B-5) ___ 5B / (B-5) = A

(20/B) - (20/A) = 1 ___ (20/B) - {20 / [5B / (B-5)]} = 1 ___ 100 - 20B + 100 = 5B ___ 200 = 25B ___ 8 = B

A = (5 * 8) / (8 - 5) = 40/3