Answer:
See explanation
Step-by-step explanation:
An aquarium tank can hold V liters of water.
The first pipe alone can fill the tank in [tex]t_1[/tex] minutes. Then the first pipe fills [tex]\dfrac{V}{t_1}[/tex] liters per minute.
The second pipe can fill the tank in minutes by itself. Then the first pipe fills [tex]\dfrac{V}{t_2}[/tex] liters per minute.
When both pipes are working together, they fill
[tex]\dfrac{V}{t_1}+\dfrac{V}{t_2}[/tex] liters per minute.
Working together they need
[tex]\dfrac{V}{\frac{V}{t_1}+\frac{V}{t_2}}=\dfrac{V}{\frac{Vt_2+Vt_1}{t_1t_2}}=\dfrac{Vt_1t_2}{V(t_1+t_2)}=\dfrac{t_1t_2}{t_1+t_2}[/tex]
minutes to fill the aquarium.
Just substitute given times to find the common time needed.
