Children's 31961

The pool for swimmers has dimensions of 25m, 10m, and 2.8m, and the children's pool is only 10m, 4m, and 1m. The pump will change all the water in the swimming pool in 9 hours. How long does it take for the same pump to pump out the water in the children's pool? The water in both pools reaches 3 dm below the edge.

Result

t = 0:24 h

Step-by-step explanation:

$$\begin{gathered} a=25\text{m} \\ x=10\text{m} \\ {t}_1=9\text{h} \\ {c}_1=3\text{dm}\to \text{m}=3:10\text{m}=0.3\text{m} \\ {V}_1=a\cdot b\cdot (c-c_1)=25\cdot 10\cdot (2.8-0.3)=625{\text{m}}^3 \\ {V}_2=x\cdot y\cdot (z-c_1)=10\cdot 4\cdot (1-\frac{3}{10})=28{\text{m}}^3 \\ t=t_1\cdot \frac{V_2}{V_1}=9\cdot \frac{28}{625}=\frac{9\cdot 28}{625}=\frac{252}{625}=0.4032=0:24\text{h} \end{gathered}$$

Try another example