SOLUTION: Please help me figure this out. A cold faucet can fill a sink in 12 minutes, and a hot water faucet can fill it in 15. The drain can empty the sink in 25 minutes. If both fau

Algebra ->  Systems-of-equations -> SOLUTION: Please help me figure this out. A cold faucet can fill a sink in 12 minutes, and a hot water faucet can fill it in 15. The drain can empty the sink in 25 minutes. If both fau      Log On


   

Question 121540: Please help me figure this out.
A cold faucet can fill a sink in 12 minutes, and a hot water faucet can
fill it in 15. The drain can empty the sink in 25 minutes. If both
faucets are on and the drain is open, how long will it take to fill
the sink?
Answers:
a) 8 4/13 minutes
b) 8 9/10 minutes
c) 9 1/11 minutes
d) 9 8/9 minutes
e) 10 2/15 minutes
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A cold faucet can fill a sink in 12 minutes, and a hot water faucet can
fill it in 15. The drain can empty the sink in 25 minutes. If both
faucets are on and the drain is open, how long will it take to fill
the sink?
:
Let t = time required to fill the sink, as described
:
Let the full sink = 1
:
Filling is plus, draining is minus
:
Cold faucet + Hot faucet - drain = Full sink
t%2F12 + t%2F15 - t%2F25 = 1
:
Find a common denominator, multiply equation by 900
900*t%2F12 + 900*t%2F15 - 900*t%2F25 = 900(1)
Cancel out the denominators and we have;
:
75t + 60t - 36t = 900
:
99t = 900
t = 900%2F99
t = 9.1 min or 9 1%2F11 min
:
:
Check solution using the decimal
9.1%2F12 + 9.1%2F15 - 9.1%2F25 = 1
.758 + .607 - .364 ~ 1.00; confirms our solution