Four-fifths of the pool

The rectangular pool, with bottom dimensions of 12 m and 25m, is 200 cm deep. The first faucet flows 2.4 hl per minute and the second 6 l per 1 second. How long will it take for the pool to be filled to four-fifths of its height?

Final Answer:

t =  800 min

Step-by-step explanation:

$$\begin{gathered} a=12\text{m} \\ b=25\text{m} \\ c=200\text{cm}\to \text{m}=200:100\text{m}=2\text{m} \\ {c}_1=\frac{4}{5}\cdot c=\frac{4}{5}\cdot 2=\frac{4\cdot 2}{5}=\frac{8}{5}=1.6\text{m} \\ V=a\cdot b\cdot c_1=12\cdot 25\cdot \frac{8}{5}=480{\text{m}}^3 \\ {V}_1=2.4\text{hl}\to {\text{m}}^3=2.4:10{\text{m}}^3=0.24{\text{m}}^3 \\ {V}_2=6\cdot 60=360\text{l} \\ {V}_3=V_2\to {\text{m}}^3=V_2:1000{\text{m}}^3=360:1000{\text{m}}^3=0.36{\text{m}}^3 \\ t=\frac{V}{V_1+V_3}=\frac{480}{\frac{6}{25}+\frac{9}{25}}=800\text{min} \end{gathered}$$

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