Block-shaped 17203

A block-shaped pool with bottom dimensions of 12 m and 20 m and a depth of 2 m is filled with two pipes. The first pipe flows 6 l of water per second, the second 2.4 hl per minute. How many hours and minutes will the pool be filled 40 cm below the edge?

Result

t = 10:40 hh:mm

Step-by-step explanation:

$$\begin{gathered} a=12\text{m} \\ b=20\text{m} \\ c=2\text{m} \\ {c}_2=40\text{cm}\to \text{m}=40:100\text{m}=0.4\text{m} \\ {V}_1=6\text{l}\to {\text{m}}^3=6:1000{\text{m}}^3=0.006{\text{m}}^3 \\ {V}_2=2.4\text{hl}\to {\text{m}}^3=2.4:10{\text{m}}^3=0.24{\text{m}}^3 \\ {Q}_1=V_1=0.006=\frac{3}{500}=0.006{\text{m}}_3\text{/s} \\ {Q}_2=V_2/60=0.24/60=\frac{1}{250}=0.004{\text{m}}_3\text{/s} \\ V=a\cdot b\cdot (c-c_2)=12\cdot 20\cdot (2-0.4)=384{\text{m}}^3 \\ {t}_1=V/(Q_1+Q_2)=384/(0.006+0.004)=38400\text{s} \\ t=t_1\to \text{h}=t_1:3600\text{h}=38400:3600\text{h}=10.667\text{h}=10.66667=10:40\text{hh}:\text{mm} \end{gathered}$$

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