SOLUTION: A faucet can fill a tub in 12 mins. The leaky drain can empty the tube in. 30 mins. If the faucet is on and the drain is leaking, how long would it take to fill the tub?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: A faucet can fill a tub in 12 mins. The leaky drain can empty the tube in. 30 mins. If the faucet is on and the drain is leaking, how long would it take to fill the tub?       Log On


   



Question 1134494: A faucet can fill a tub in 12 mins. The leaky drain can empty the tube in. 30 mins. If the faucet is on and the drain is leaking, how long would it take to fill the tub?
Found 3 solutions by mathsolverplus, ankor@dixie-net.com, ikleyn:
Answer by mathsolverplus(88) About Me  (Show Source):
You can put this solution on YOUR website!
Let's see what happens under a minute.
Filling rate = 1/12min
Draining rate = - 1/30min
Together: 1/12-1/30 = 1/x, where x represents the time it takes to fill the tub.
1%2F12-1%2F30=1%2Fx
5%2F60-2%2F60=1%2Fx
3%2F60=1%2Fx
1%2F20=1%2Fx
x=20
It would take 20 minutes to fill the tub.
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Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A faucet can fill a tub in 12 mins.
The leaky drain can empty the tube in. 30 mins.
If the faucet is on and the drain is leaking, how long would it take to fill the tub?
:
let t = time to fill the tub in these conditions
let the full tub = 1
:
A typical mixture problem
t%2F12 - t%2F30 = 1
multiply equation by 60
60*t%2F12 - 60* t%2F30 = 60(1)
cancel the denominators
5t - 2t = 60
3t = 60
t = 60/3
t = 20 min to fill the tub

Answer by ikleyn(52884) About Me  (Show Source):
You can put this solution on YOUR website!
.

It is a standard and typical joint work problem.

There is a wide variety of similar solved joint-work problems with detailed explanations in this site.  See the lessons
    - Using Fractions to solve word problems on joint work
    - Solving more complicated word problems on joint work
    - Selected joint-work word problems from the archive


Read them and get be trained in solving joint-work problems.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic
"Rate of work and joint work problems"  of the section  "Word problems".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.