Workers

The first worker can complete a job in 40 hours, the second in 50 hours, and the third in 80 hours. How long will it take them to complete the job if they all work together?

Final Answer:

x =  17.3913 h

Step-by-step explanation:

$$\begin{gathered} a=40\text{h} \\ b=50\text{h} \\ c=80\text{h} \\ h=\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{1}{40}+\frac{1}{50}+\frac{1}{80}=\frac{10}{400}+\frac{8}{400}+\frac{5}{400}=\frac{10+8+5}{400}=\frac{23}{400}=0.0575 \\ x\cdot h=1 \\ x=\frac{1}{h}=\frac{1}{\frac{23}{400}}=\frac{400}{23}\text{h}=17.3913\text{h} \end{gathered}$$

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