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The problem reads:

**La empresa de conservas "Del Valle" tiene cinco máquinas que envasan 1000 latas de conservas de duraznos en 8 horas. ¿Cuántas horas demorará el doble de la cantidad de máquinas en envasar el triple de cantidad de latas de conservas de duraznos?**

Translation:
The company "Del Valle" has five machines that pack 1000 cans of peach preserves in 8 hours. How many hours will it take for double the number of machines to pack triple the number of cans?

### Solution:
Let's break this down step by step.

1. **Initial condition**: 
   5 machines pack 1000 cans in 8 hours.

   So, the rate of packing is:
   \[
   \text{Rate of 1 machine} = \frac{1000 \text{ cans}}{8 \text{ hours} \times 5 \text{ machines}} = \frac{1000}{40} = 25 \text{ cans per hour per machine.}
   \]

2. **New condition**:
   - Double the number of machines: \( 5 \times 2 = 10 \text{ machines}. \)
   - Triple the number of cans: \( 1000 \times 3 = 3000 \text{ cans}. \)

3. **How long will it take?**:
   The new rate with 10 machines is:
   \[
   \text{Rate of 10 machines} = 10 \times 25 = 250 \text{ cans per hour}.
   \]

   To pack 3000 cans:
   \[
   \text{Time required} = \frac{3000 \text{ cans}}{250 \text{ cans per hour}} = 12 \text{ hours}.
   \]

### Final Answer:
It will take **12 hours** for 10 machines to pack 3000 cans.

Would you like further details or have any questions?

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Here are 5 related questions to extend this concept:
1. How long would it take for one machine to pack 1000 cans?
2. If only 3 machines were used, how long would it take to pack 2000 cans?
3. What is the rate of packing if the machines were more efficient, packing 50 cans per hour each?
4. How would the time change if the machines packed 4000 cans instead of 3000 with 10 machines?
5. How many machines are needed to pack 3000 cans in 6 hours?

**Tip**: Always try to first find the rate per machine when solving time-rate problems, as it simplifies calculations when changing the number of machines or items.

La empresa de conservas "Del Valle" tiene cinco máquinas que envasan 1000 latas de conservas de duraznos en 8 horas. ¿Cuántas horas demorará el doble de la cantidad de máquinas en envasar el triple de cantidad de latas de conservas de duraznos?

Solve the problem of calculating how long it will take for double the machines to pack triple the number of cans. Learn how rates and proportions help to determine time in a machine work scenario. Suitable for students in Grades 8-10.

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