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 result:

t =  40.9091 min

Solution:

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

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