Three pumps together

One pump fills the tank in 1.5 hours, the second in 2 hours, and the third in 3 hours 20 minutes. How many minutes will the tank fill with three pumps if they work simultaneously?

Correct answer:

t =  40.9091 min

Step-by-step explanation:

$$\begin{gathered} a=1.5\text{h}\to \text{min}=1.5\cdot 60\text{min}=90\text{min} \\ b=2\text{h}\to \text{min}=2\cdot 60\text{min}=120\text{min} \\ c=h_2\min (3+20/60)=200 \\ s=\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{1}{90}+\frac{1}{120}+\frac{1}{200}=\frac{20}{1800}+\frac{15}{1800}+\frac{9}{1800}=\frac{20+15+9}{1800}=\frac{44}{1800}=\frac{11}{450}\doteq 0.0244 \\ t=1/s=1/\frac{11}{450}=1:\frac{11}{450}=1\cdot \frac{450}{11}=\frac{1\cdot 450}{11}=\frac{450}{11}=\frac{450}{11}\text{min}=40.9091\text{min} \end{gathered}$$

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