Leaking swimming pool

Between 10 pm and 7:10 am, the water level in a swimming pool decreased by 5/12 inches. Assuming that the water level decreased constantly, how much did it drop each hour?

Correct answer:

h =  1/22 inch/h

Step-by-step explanation:

$$\begin{gathered} t_1=12-10=2\text{h} \\ {t}_2=7\frac{10}{60}=7+\frac{10}{60}=\frac{7\cdot 60+10}{60}=\frac{420+10}{60}=\frac{430}{60}=\frac{43}{6}\doteq 7.1667\text{h} \\ t=t_1+t_2=2+\frac{43}{6}=\frac{2\cdot 6}{6}+\frac{43}{6}=\frac{12}{6}+\frac{43}{6}=\frac{12+43}{6}=\frac{55}{6}\doteq 9.1667\text{h} \\ H=\frac{5}{12}\doteq 0.4167\text{inch} \\ h=H/t=\frac{5}{12}/\frac{55}{6}=\frac{5}{12}:\frac{55}{6}=\frac{5}{12}\cdot \frac{6}{55}=\frac{5\cdot 6}{12\cdot 55}=\frac{30}{660}=\frac{1}{22}\text{inch/h}=0.0455\text{inch/h} \end{gathered}$$

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