Question

A swimming pool holds 585,000 liters of water. When the pool is completely full, the first pipe alone can empty it in 130 minutes, and the second pipe alone can empty it in 195 minutes. When both pipes are draining together, how long does it take them to empty the pool?

Answer 1

We will have the following:

First, we find the draining rate for each individual pipe:

$\begin{cases}p_1=(585000l)/(130\min )\Rightarrow p_1=4500l/\min \\ \\ p_2=(585000l)/(195\min )\Rightarrow p_2=3000l/\min \end{cases}$

Now, we will have that their combined draining rate will be:

$p_3=p_1+p_2\Rightarrow p_3=4500l/\min +3000l/\min$$\Rightarrow p_3=7500l/\min$

Now, we determine the time it takes for both pipes to drain it, that is:

$x=\frac{585000l\cdot1\min}{7500l}\Rightarrow x=78\min$

So, it will take 78 minutes for both pipes to fully drain it.