SOLUTION: the hot water faucet can fill a bathtub in 9 min and the cold water faucet can fill the bathtub in 12 min. the drain can empty the bathtub in 18 min. if the bathtub is empty, how l

Question 1117460: the hot water faucet can fill a bathtub in 9 min and the cold water faucet can fill the bathtub in 12 min. the drain can empty the bathtub in 18 min. if the bathtub is empty, how long will it take to fill the bathtub if both hot and cold faucets are on and the drain is open???
Found 2 solutions by ikleyn, solver91311:
Answer by ikleyn(52832)   (Show Source): You can put this solution on YOUR website!
.

The hot water faucet fills of the bathtub volume per minute. The cold water faucet fills of the bathtub volume per minute. The drain takes out of the bathtub volume per minute. The net inflow rate is = = of the bathtub volume per minute. Hence, it will take minutes = minutes = 7 minutes and 12 seconds to fill the bathtub if both hot and cold faucets are on and the drain is open.

Solved.

----------------
It is a typical and standard 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.

Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

If the hot water tap can fill the bathtub in 9 minutes, then the hot water tap must fill of the bathtub in one minute. Likewise, the cold tap fills of the tub in one minute and the drain empties of the tub in one minute. So altogether:

of the tub gets filled (because this is clearly a positive number) every minute, and it will take the reciprocal of the above sum in minutes to fill the tub, so since the lowest common denominator is 36:

It will take minutes or 7 minutes and 12 seconds to fill the tub if both taps and the drain are open.

John

My calculator said it, I believe it, that settles it

RELATED QUESTIONS
A bathtub can be filled by the cold water faucet in 12 minutes and by the hot water... (answered by stanbon)
A bathtub can be filled by the cold water faucet in 8 minutes and by the hot water faucet (answered by Alan3354)
a bathtub can be filled by the cold water faucet in eight minutes and by the hot water... (answered by nerdybill)
by itself a cold water faucet can fill a tub in 9 min. By itself, a hot water faucet can (answered by valdez62)
Used by itself, the cold water faucet can fill a bathtub in 12 minutes. It takes 15... (answered by ptaylor)
If a hot-water faucet can fill a sink in 9 min. and a cold-water faucet can fill it in 6. (answered by Alan3354)
A bathtub can be filled in 20 minutes with both faucets running. If the cold water faucet (answered by scott8148)
A bathtub can be filled by the cold water faucet in 13 minutes and by the hot water... (answered by josmiceli)
A bathtub can be filled by the cold water faucet in 5 minutes and by the hot water faucet (answered by josmiceli)