A fountain has two basins, one above and one below, each of which has three outlets. The first outlet of the top basin fills the lower basin in two hours, the second in three hours, and the third in four hours. When all three upper outlets are shut, the first outlet of the lower basin empties it in three hours, the second in four hours, and the third in five hours. If all the outlets are opened, how long will it take for the lower basin to fill?

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pedrocarratore pedrocarratore · Answer 1 · 2020-02-14T05:18:51+01:00

Answer:

3.33 hours

Step-by-step explanation:

Let 'V' be the volume of the lower basin, the flow rate at which the three top outlets fill the basin when all three are open is:

[tex]Q_{in}=\frac{V}{2} +\frac{V}{3} +\frac{V}{4}\\ Q_{in}=1.08333\ V/hour[/tex]

The flow rate at which the three bottom outlets empty the basin when all three are open is:

[tex]Q_{out}=\frac{V}{3} +\frac{V}{4} +\frac{V}{5}\\ Q_{out}=0.78333\ V/hour[/tex]

Assuming it is initially empty, the time it takes to fill the lower basin with all outlets open is:

[tex]t=\frac{V}{Q_{in}- Q_{out}} \\t= \frac{V}{1.08333-0.78333\ V}\\t=3.33\ hours[/tex]

It takes 3.33 hours.