5. Each of two ants, Fat and Thin, needs to transport 150 g of cargo from point $A$ (where they are currently located) to point $B$, the distance between which is 15 meters. The Fat ant walks at a speed of 3 m/min but can carry 5 g of cargo, while the Thin ant walks at a speed of 5 m/min but can carry only 3 g of cargo. Who will deliver all their cargo to point $B$ faster? The speed of an ant with cargo is the same as the speed of an ant without cargo.
Answer: The Fat one will finish 2 minutes earlier.

Solution: To deliver the cargo, the Fat one needs to make 30 trips from point $A$ to point $B$ and 29 return trips from point $B$ to point $A$. One trip takes him 5 minutes, so the total time will be $5 \cdot (30 + 29) = 295$ minutes. The Thin ant needs to make 50 trips from point $A$ to point $B$ and 49 return trips from point $B$ to point $A$. One trip takes him 3 minutes, so the total time will be $3 \cdot (50 + 49) = 297$ minutes. Therefore, the Fat one will finish his work earlier.

Comment: Another possible solution is as follows. If both ants were at point $B$, they would complete the work in the same amount of time: the Fat one would need to make 60 trips at 5 minutes each, and the Thin one would need to make 100 trips at 3 minutes each. Since the ants are already at point $A$, the Fat one's time is reduced by 5 minutes, and the Thin one's time is reduced by 3 minutes. Thus, the Fat one will finish the work earlier.

## Grading Criteria.

- Correct solution - 7 points.
- Arithmetic error in calculations, but the logic is correct - 5-6 points.
- Correct precise answer (The Fat one will finish 2 minutes earlier) without justification - 2 points.
- Error in calculating the number of trips - they assume the number of trips there and back should be the same (i.e., they assume the Fat one needs 30 round trips and the Thin one needs 50 round trips, thus getting $30 \cdot 10 = 300$ minutes for the Fat one and $50 \cdot 6 = 300$ minutes for the Thin one), resulting in an incorrect answer that the time taken by the ants will be the same - $\mathbf{1}$ point.
- Only the correct answer (The Fat one will finish earlier) - $\mathbf{0}$ points.