MO Z8–I–4 2017

Robots Robert and Hubert assemble and disassemble coffee grinders. Each of them, however, assembles a grinder four times faster than the other one disassembles it. When they came to the workshop in the morning, several grinders were already assembled there.

At 9:00 Hubert started to assemble and Robert to disassemble, exactly at 12:00 Hubert finished assembling one grinder and Robert finished disassembling another. Together during this shift 27 grinders were added.

At 13:00 Robert started to assemble and Hubert to disassemble, exactly at 19:00 Robert finished assembling the last grinder and Hubert finished disassembling another. Together during this shift 120 grinders were added.

In how long does Hubert assemble a grinder? In how long does Robert assemble it?

Final Answer:

H =  5 min
R =  2.25 min

Step-by-step explanation:

$$\begin{gathered} 27=(h-h/4)\cdot (12.00-9.00) \\ h=12 \\ H=60/h=60/12=5\text{min} \end{gathered}$$

$$\begin{gathered} 120=(r-r/4)\cdot (19.00-13.00) \\ 120=3/4r\cdot 6 \\ r=80/3=\frac{80}{3}\doteq 26.6667 \\ R=60/r=60/26.6667=2.25\text{min} \end{gathered}$$

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