Basement pump water

After the flood, the Nováks would pump water out of the basement with one pump in 120 minutes, the second in 300 minutes, and the third in 600 minutes. How many minutes will it take them to pump the water out of the basement if they use all the pumps at once?

Final Answer:

t =  75 min

Step-by-step explanation:

$$\begin{gathered} t_1=120\text{min} \\ {t}_2=300\text{min} \\ {t}_3=600\text{min} \\ q=\frac{1}{t_1}+\frac{1}{t_2}+\frac{1}{t_3}=\frac{1}{120}+\frac{1}{300}+\frac{1}{600}=\frac{5}{600}+\frac{2}{600}+\frac{1}{600}=\frac{5+2+1}{600}=\frac{8}{600}=\frac{1}{75}\doteq 0.01331\text{/min} \\ t\cdot q=1 \\ t=1/q=1/\frac{1}{75}=1:\frac{1}{75}=1\cdot \frac{75}{1}=\frac{1\cdot 75}{1}=\frac{75}{1}=75\text{min} \end{gathered}$$

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