Excavation by gentlemen

The site manager, based on the length of the excavation, estimated that the whole excavation for laying a plastic pipe bringing water to the kindergarten building could be carried out by Mr. Demeter together with Mr. Vondrák in 1.2 shifts. From experience he knew that the difference between the work performance of Mr. Demeter and Mr. Vondrák per 1 shift can be expressed as one sixth of the length of the excavation. In how many shifts was Mr. Demeter able to carry out the entire excavation alone, and Mr. Vondrák alone, if you know that Mr. Demeter was a more efficient digger than Mr. Vondrák?

Final Answer:

d =  2
v =  3

Step-by-step explanation:

$$\begin{gathered} 1.2\cdot (1/d+1/v)=1 \\ 1/d=1/6+1/v \\ 1.2\cdot (a+b)=1 \\ a=1/6+b \\ a=1/2=\frac{1}{2}=0.5 \\ b=1/3=\frac{1}{3}\doteq 0.3333 \\ d=1/a=1/0.5=2 \end{gathered}$$

$v=1/b=1/0.3333=3$

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