Three workshops

One workshop can complete the task in 48 days, the second in 30 days and the third in 20 days. In how many days would the task be completed if all workshops worked?

Correct result:

t =  9.6 d

Solution:

$$\begin{gathered} t_1=48 \\ {t}_2=30 \\ {t}_3=20 \\ t\cdot (1\mathrm{/}{t}_1+1\mathrm{/}{t}_2+1\mathrm{/}{t}_3)=1 \\ t\cdot (1\mathrm{/}48+1\mathrm{/}30+1\mathrm{/}20)=1 \\ 25t=240 \\ t={\displaystyle \frac{48}{5}}=9.6={\displaystyle \frac{48}{5}}\text{ d}=9.6\text{ d} \end{gathered}$$

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