SOLUTION: It takes 10 minutes to fill Alisha's bathtub and 12 minutes to empty it. How long would it take to fill if the drain were accidentally open. I understand how to set this problem.

Algebra ->  Rational-functions -> SOLUTION: It takes 10 minutes to fill Alisha's bathtub and 12 minutes to empty it. How long would it take to fill if the drain were accidentally open. I understand how to set this problem.       Log On


   

Question 401238: It takes 10 minutes to fill Alisha's bathtub and 12 minutes to empty it. How long would it take to fill if the drain were accidentally open. I understand how to set this problem.
Found 2 solutions by ankor@dixie-net.com, josmiceli:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
It takes 10 minutes to fill Alisha's bathtub and 12 minutes to empty it.
How long would it take to fill if the drain were accidentally open.
:
Let t = time to fill the tub with the drain open
Let the full tub = 1
:
+ is fill, - is drain
:
t%2F10 - t%2F12 = 1
multiply 60:
60*t%2F10 - 60*t%2F12 = 60(1)
cancel the denominators, results:
6t - 5t = 60
t = 60 minutes to fill with drain left open

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Rate of filling = R%5B1%5D+=+1%2F10 (1 tubful/10 min)
Rate of emptying: R%5B2%5D+=+1%2F12 (1 tubful/12 min)
Let R%5B3%5D = rate with both open
---------------------------
R%5B3%5D+=+R%5B1%5D+-+R%5B2%5D
R%5B3%5D+=+1%2F10+-+1%2F12
R%5B3%5D+=+6%2F60+-+5%2F60
R%5B3%5D+=+1%2F60
1%2F60+=+1%2Ft (1 tubful/t minutes)
t+=+60 min
It will take 1 hour to fill the tub with drain open