Bucket tap filling

A bucket is filled by one tap in 4 minutes and by another tap in 3 minutes. How many minutes will it take to fill 5 buckets if both taps run simultaneously?

Result

t = 0:09 h

Step-by-step explanation:

$$\begin{gathered} t_1=4\text{min}\to \text{h}=4:60\text{h}=0.06667\text{h} \\ {t}_2=3\text{min}\to \text{h}=3:60\text{h}=0.05\text{h} \\ n=5 \\ T\cdot (1/t_1+1/t_2)=1 \\ T\cdot (1/0.066666666666667+1/0.05)=1 \\ 35T=1 \\ T=\frac{1}{35}=0.02857143 \\ T=\frac{1}{35}\doteq 0.028571 \\ t=n\cdot T=5\cdot 0.0286=0.14286=0:09\text{h} \end{gathered}$$

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