Two diggers

There are two diggers. One digger digs a pit 77 hours per second, digging 1.2 times faster.

a) how long did digging a pit with a second digger take?
b) how long did it take to dig together?

Correct answer:

b =  64.17 h
s =  35 h

Step-by-step explanation:

$$\begin{gathered} a=77\text{h} \\ b=a/1.2=77/1.2=64.17\text{h} \end{gathered}$$

$$\begin{gathered} s\cdot (1/a+1/b)=1 \\ s\cdot (1/77+1/64.166666666667)=1 \\ 2.2s=77 \\ s=\frac{77}{2.2}=35 \\ s=35=35\text{h} \end{gathered}$$

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