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

At 9:00, Hubert started assembling and Robert disassembling, and precisely at 12:00, Hubert finished assembling a coffee grinder and Robert disassembling another one. In total, 27 coffee grinders were added during this shift.

At 13:00, Robert started assembling and Hubert disassembling, and precisely at 19:00, Robert finished assembling the last coffee grinder and Hubert disassembling another one. In total, 120 coffee grinders were added during this shift.

How long does it take for Hubert to assemble a coffee grinder? How long does it take for Robert to assemble one?

(K. Pazourek)

Hint. How many coffee grinders are added per hour in each shift?
In the morning three-hour shift, 27 coffee mugs were added, which corresponds to $27: 3=9$ coffee mugs per hour. Since Robert disassembles four times slower than Hubert assembles, Hubert alone would assemble 9 coffee mugs in $\frac{3}{4}$ of an hour, i.e., 45 minutes. Therefore, Hubert assembles one coffee mug in $45: 9=5$ minutes.

In the afternoon six-hour shift, 120 coffee mugs were added, which corresponds to $120: 6=20$ coffee mugs per hour. This time, Robert assembles and Hubert disassembles, so Robert alone would assemble 20 coffee mugs in $\frac{3}{4}$ of an hour, i.e., 45 minutes. Therefore, Robert assembles one coffee mug in $45: 20=2.25$ minutes, i.e., 2 minutes and 15 seconds.

Another solution. If $h$ represents the number of coffee mugs Hubert assembles per hour, and $r$ represents the number of coffee mugs Robert assembles per hour, then in one hour Hubert disassembles $\frac{1}{4} r$ coffee mugs and Robert disassembles $\frac{1}{4} h$ coffee mugs. The information from the problem leads to the equations:

$$
\begin{aligned}
& 3\left(h-\frac{1}{4} h\right)=27 \\
& 6\left(r-\frac{1}{4} r\right)=120 .
\end{aligned}
$$

The solution to the first equation is $h=12$, so Hubert assembles 12 coffee mugs per hour, i.e., 60 minutes. Hubert assembles one coffee mug in $60: 12=5$ minutes. The solution to the second equation is $r=\frac{80}{3}$, so Robert assembles 80 coffee mugs in 3 hours, i.e., 180 minutes. Robert assembles one coffee mug in $180: 80=2.25$ minutes.