Question

One pipe can fill a swimming pool in 10 hours, while another pipe can empty the pool in 15 hours. How long would it take to fill the pool if both pipes were accidentally left open?

Answer 1

It will take 30 hours to fill the pool if both pipes were accidentally left open

Solution:

Given, One pipe can fill a swimming pool in 10 hours,  

While another pipe can empty the pool in 15 hours.  

We have to find how long would it take to fill the pool if both pipes were accidentally left open?

Now, work done by 1st pipe in 1 hour $= \frac{1}{10}$

And, work done by 2nd pipe in 1 hour $= \frac{-1}{15}$

Here negative sign represents "empties the pipe"

Together work done in 1 hour = work done by 1st pipe in 1 hour + work done by 2nd pipe in 1 hour

$=\frac{1}{10}+\frac{-1}{15}=\frac{3-2}{30}=\frac{1}{30}$

Now, time required to fill tank together $=\frac{1}{\text {work done in } 1 \text { hour }}=\frac{1}{\frac{1}{30}}=30 \text { hours. }$

Hence, together they will fill the tank in 30 hours.