SOLUTION: a pipe can fill a water tank in 8 hours. Due to a leak in the bottom of the water tank it is filled in 10 hours. If the water tank is full how much time will the leak take to empty

Question 1072941: a pipe can fill a water tank in 8 hours. Due to a leak in the bottom of the water tank it is filled in 10 hours. If the water tank is full how much time will the leak take to empty it?

Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.

Let P be the rate of the pipe (in the unit "tank volume per hour").
Let L be the rate of the leak (in the same unit).


Then you have two equations:

P - L =     (1)   (The pipe fills the tank in 10 hours, when the leak is in action).

P = .        (2)   ("The pipe can fill a water tank in 8 hours.")


Substitute (2) into equation (1). You will get

 - L =   --->  L =  =  = .


So, due to the leak, amount of water of  of the tank volume goes out.

It means, that the full tank will become empty in 40 hours due to the leak.

Solved.

It is a typical joint work problem.

For a wide variety of similar solved joint-work problems with detailed explanations 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
in this site.

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".

RELATED QUESTIONS
A pump can fill a tank with water in 2 hours. Because of a leak in the tank it was... (answered by macston)

An electric pump can fill a tank in 3 hours. Because of a leak in the tank, it took 3... (answered by josgarithmetic,lwsshak3)

Water can be pumped into or out of a tank via pipes A, B, and C. Pipe A can fill the tank (answered by Edwin McCravy)

A water tank can be filled by an inlet in 8 hours. It takes twice the long for the outlet (answered by josgarithmetic)

a pipe can fill a tank in 15 hours. The tank develop a hole and 10% of water leaks out .... (answered by ankor@dixie-net.com)

With 2 inflowing pipes open, a water tank can be filled in four hours. if the larger pipe (answered by ikleyn,greenestamps)

A pipe can fill a water tank in 24 hours. The drain can drain the tank in 18 hours. If... (answered by richwmiller)

Pipe A can fill a tank in 8 hours. When both A and pipe B are used th tank is filled in 5 (answered by ankor@dixie-net.com)

A water tank is being filled by two inlet pipes. Pipe A can fill the tank in half the... (answered by lwsshak3)