## Task 1 - 190711

A group of 8 students excavates a trench in the production work at their godfather company that is 30 cm wide, 60 cm deep, and 20 m long. A second group of 6 students excavates a trench that is 25 cm wide, 50 cm deep, and 22 m long.

It is assumed that each of the 14 students requires the same amount of time to excavate equal volumes (with the time required to excavate a specific volume being the same for all students).

Which of the two groups will require less time to excavate their trench under these assumptions?
The volume of the trench of the first group is $(3 \cdot 6 \cdot 200) \mathrm{dm}^{3}=3600 \mathrm{dm}^{3}$; for each of the 8 students in this group, therefore, a volume of (3600:8) $\mathrm{dm}^{3}=450 \mathrm{dm}^{3}$ needs to be excavated.

The volume of the trench of the second group is $(2.5 \cdot 5 \cdot 220) \mathrm{dm}^{3}=2750 \mathrm{dm}^{3}$; for each of the 6 students in this group, therefore, a volume of (2750:6) $\mathrm{dm}^{3}=458 \frac{1}{3} \mathrm{dm}^{3}$ needs to be excavated.

If each student worked until they had excavated $458 \mathrm{dm}^{3}$, then the first group is finished, but the second group is not. Therefore, the first group requires less time than the second.