SOLUTION: An inlet pipe can fill a tank in 15 minutes. A drain can empty the tank in 18 minutes. If the tank is empty, and both the pipe and drain are open, how long will it take before the

Algebra ->  Human-and-algebraic-language -> SOLUTION: An inlet pipe can fill a tank in 15 minutes. A drain can empty the tank in 18 minutes. If the tank is empty, and both the pipe and drain are open, how long will it take before the       Log On


   



Question 1124078: An inlet pipe can fill a tank in 15 minutes. A drain can empty the tank in 18 minutes. If the tank is empty, and both the pipe and drain are open, how long will it take before the tank overflows?
Found 3 solutions by ikleyn, FrankM, MathTherapy:
Answer by ikleyn(52767) About Me  (Show Source):
You can put this solution on YOUR website!
.
The inlet pipe fills  1%2F15  of the tank volume per minute.


The drain pipe drains  1%2F18 of the tank volume per minute.


When both pipes are open,  then  the net inflow rate is   1%2F15 - 1%2F18 = 6%2F90+-+5%2F90 = 1%2F90 of the tank volume per minute.


Hence, it will take 90 minutes to fill the tank, when both pipes are working.

Solved.

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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.


Answer by FrankM(1040) About Me  (Show Source):
You can put this solution on YOUR website!
The fill rate is 4 tanks/hour
The drain rate is 3-1/3 tanks per hour.
The 'accumulation rate' is therefore 2/3 tank per hour, and it will take 1.5 hours to fill.

Proof - this is 90 minutes. In 90 minutes, the inlet can fill the tank 6 times, but the drain will let 5 tanks out.

Answer by MathTherapy(10549) About Me  (Show Source):
You can put this solution on YOUR website!
An inlet pipe can fill a tank in 15 minutes. A drain can empty the tank in 18 minutes. If the tank is empty, and both the pipe and drain are open, how long will it take before the tank overflows?
matrix%281%2C3%2C+1%2F15+-+1%2F18%2C+%22=%22%2C+1%2FT%29.
Solve for T to get: