Reconstructing highway

Three groups take turns reconstructing one piece of highway. The first group would finish the job themselves in 40 working days. The second group is in 24 working days, and the third group is in 30 working days. How many days do you do it together?

Final Answer:

t =  10 d

Step-by-step explanation:

$$\begin{gathered} a=40\text{d} \\ b=24\text{d} \\ c=30\text{d} \\ q=\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{1}{40}+\frac{1}{24}+\frac{1}{30}=\frac{3}{120}+\frac{5}{120}+\frac{4}{120}=\frac{3+5+4}{120}=\frac{12}{120}=\frac{1}{10}=0.11\text{/d} \\ t\cdot q=1 \\ t=1/q=1/0.1=10\text{d} \end{gathered}$$

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