Question

One hose can fill a small swimming pool in 70 minutes. A larger hose can fill the pool in 55 minutes. How long will it take the two hoses to fill the pool workingtogether?Do not do any rounding.

Answer 1

To determine the time it takes for the two hoses to fill the pool, we have the equation below:

$\frac{1}{70}+\frac{1}{55}=\frac{1}{t}$

where t = time in minutes for the two hoses to fill the poll.

Let's add the fractions on the left side by applying the Butterfly Method.

$\begin{gathered} \frac{1(55)+1(70)}{70(55)}=\frac{1}{t} \\ \frac{55+70}{3850}=\frac{1}{t} \\ \frac{125}{3850}=\frac{1}{t} \end{gathered}$

Then, let's cross multiply.

$125t=3850$

Lastly, divide both sides by 125.

$\begin{gathered} \frac{125t}{125}=\frac{3850}{125} \\ t=30.8\min \end{gathered}$

Hence, it will only take 30.8 minutes for the two hoses together to fill the pool.