an inlet pipe can fill a pool in 12 hrs, the outlet pipe can empty the pool in 15 hours, both pipes are left open how long will it take to fill the pool?

Question

There are two pipes and I am required to answer how long it will take to fill up the pool, if both are left open, and i do not know how to set that up nor solve it

Answer 1

Hi Lisset, this is a typical work problem. The inlet pipe can fill the pool in 12 hours, that means it can fill 1/12 of the pool in one hour.

 

The outlet pipe can empty the pool in 15 hours, that means it can empty 1/15 of the pool in one hour.

 

We set up the equation: 1/12 - 1/15 = 1/x, where x is the time to completely fill the pool.

 

We need the common denominator for 12, 15, and x. The simple way to handle tis is to multiply every term by (12 * 15 * x).

 

(12 * 15 * x) * (1/12 - 1/15 = 1/x)

 

Distribute the 12 * 15 * x through the second term giving:

 

In the first term, the 12s cancel leaving 15x, in the second term, the 15s cancel leaving 12*x. In the third term, the xs cancel leaving 12 * 15, or 180.

 

This results in 15x - 12x = 180

 

3x = 180

 

x = 60, or the pool will be filled in 60 hours.

 

Questions?

Answer 2

An alternative:

 

t represents the time the pipes are open.

 

t/12 represents the amount the inlet does

t/15 represents the amount the outlet does

 

t/12 - t/15 = 1             multiply both sides by 60, LCD

5t - 4t = 60

t = 60

 

The pool fills in 60 hours.