SOLUTION: A water tank can be filled by an inlet pipe in 9 hours. It takes 4 times as long for the outlet pipe to empty the tank. How long will it take to fill the tank if both p

Algebra ->  Test -> SOLUTION: A water tank can be filled by an inlet pipe in 9 hours. It takes 4 times as long for the outlet pipe to empty the tank. How long will it take to fill the tank if both p      Log On


   

Question 1200985: A water tank can be filled by an inlet pipe in
9
hours. It takes
4
times as long for the outlet pipe to empty the tank. How long will it take to fill the tank if both pipes are open?
Found 4 solutions by josgarithmetic, ikleyn, greenestamps, math_tutor2020:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
PIPE             SPEED           TIME        VOLUME(in tanks)
Inlet             1/9              9              1
Outlet            1/36             36             1

BOTH PIPES    1%2F9-1%2F36             x              1


%281%2F9-1%2F36%29x=1
%284%2F36-1%2F36%29x=1
%283%2F36%29x=1
x%2F12=1
highlight%28x=12%29

--------------------------------------not this------------------------------------
cross%28%281%2F9%2B1%2F36%29x=1%29
cross%28%284%2F36%2B1%2F35%29x=1%29
cross%28%285%2F36%29x=1%29
cross%28x=36%2F5%29hour

Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
A water tank can be filled by an inlet pipe in 9 hours.
It takes 4 times as long for the outlet pipe to empty the tank.
How long will it take to fill the tank if both pipes are open?
~~~~~~~~~~~~~~~~~~


        The "solution" by @josgarithmetic, giving the answer  36%2F5  hours,  is incorrect and absurdist.
        I came to bring a correct solution. 


The rate of filling is  1%2F9  of the tank volume per hour.


The rate of draining is  1%2F36  of the tank volume per hour.


The net rate of filling is the difference  

    1%2F9+-+1%2F36 = 4%2F36-1%2F36 = 3%2F36 = 1%2F12  of the tank volume per hour.


It means that under given conditions, the tank will be filled in 12 hours.    ANSWER

Solved.

------------------

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 greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Here are a couple of quick informal methods for solving the problem, if a formal algebraic solution, as shown by the other tutors, is not required.

It takes the inlet pipe 9 hours to fill the pool, so it takes 4*9 = 36 hours for the drain pipe to empty it.

Consider a time length of 36 hours -- the least common multiple of 9 hours and 36 hours. In 36 hours the inlet pipe could fill the pool 4 times, while in 36 hours the drain pipe could empty it once. So in 36 hours with the inlet pipe and drain pipe both open, they could fill the pool 4-1 = 3 times.

But that means the two together could fill the one pool in 36/3 = 12 hours.

And here is another quick path to the solution, using logical reasoning.

Since the drain pipe works 1/4 as fast as the inlet pipe, when both pipes are working the pool gets filled only 3/4 as fast as when the drain pipe is closed. And since it normally takes the inlet pipe 9 hours to fill the tank, the amount of time it takes the pool to fill when the drain pipe is open is 9/(3/4) = 9*(4/3) = 12 hours.

Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

The tank can be completely filled in 9 hours.

It takes 4 times as long to empty the tank.
It takes 4*9 = 36 hours to empty the tank.

Let's say the tank was 36 gallons.

The fill rate is 36/9 = 4 gallons per hour.
Formula:
rate = (amount done)/(time)

The drain rate would be 36/36 = 1 gallon per hour.

Subtract those two rates
4-1 = 3
This indicates the net rate is +3 gallons per hour.
The plus or positive means more water enters the tank than is drained.
Overall, the tank is getting filled up even if the drain pipe is open.

If both pipes are open, then it would take 36/3 = 12 hours to fill the tank.
Formula:
time = (amount done)/(rate)

Answer: 12 hours