Question

Can someone please help me to answer this math question? Please? I will fan and give a medal...

Answer 1

A tank can be filled by one pipe in 9 minutes and drained by another pipe in 12 minutes. Write an equation that could be used to determine how long it will take to fill the tank if the two pipes are open at the same time.

Answer 2

I'm thinking...

Answer 3

ok...

Answer 4

after \(1\) minute the tank contains \(h_1-h_2\) liters of fluid, wherein
\[\begin{gathered}
{h_1} = \frac{V}{{{t_1}}},\quad {h_2} = \frac{V}{{{t_2}}} \hfill \\
\hfill \\
{t_1} = 9,\quad {t_2} = 12 \hfill \\
\end{gathered} \]
and \(V\) is the volume of the tank

Answer 5

so if \(t_0\) is the requested time, in order to fill the tank, then we can write:
\[V = {h_1}{t_0} - {h_2}{t_0} = \left( {{h_1} - {h_2}} \right){t_0}\]

Answer 6

now substituting for \(h_1,h_2\), we get:
\[V = \left( {\frac{V}{{{t_1}}} - \frac{V}{{{t_2}}}} \right){t_0}\]

Answer 7

now I simplify such formula, I divide both sides by \(V\):
\[1 = \left( {\frac{1}{{{t_1}}} - \frac{1}{{{t_2}}}} \right){t_0}\]

now I compute the LCM, and I simplify like this:
\[1 = \left( {\frac{{{t_2} - {t_1}}}{{{t_1}{t_2}}}} \right){t_0}\]

Answer 8

finally I can write this:
\[{t_0} = \frac{{{t_1}{t_2}}}{{{t_2} - {t_1}}} = \frac{{12 \times 9}}{{12 - 9}} = ...?\]

Answer 9

108/3

Answer 10

? Is that right @Michele_Laino ?