If 6 cows can eat 13 bales of hay in 5 days, how long will it take 8 cows to eat 17 bales of hay?

This problem involves finding the relationship between the number of cows, the number of bales of hay, and the time it takes for them to consume it. It's a typical work-rate problem.

### Step-by-step solution:

1. **Determine the rate of consumption for 1 cow:**

   From the given information:
   - 6 cows eat 13 bales of hay in 5 days.
   
   We can find the rate of consumption per cow per day:
   \[
   \text{Rate of 1 cow} = \frac{13 \text{ bales}}{6 \times 5 \text{ days}} = \frac{13}{30} \text{ bales per cow per day}.
   \]

2. **Find how many bales 8 cows eat per day:**

   Now that we know the consumption rate of 1 cow, we can calculate the daily consumption of 8 cows:
   \[
   \text{Daily consumption of 8 cows} = 8 \times \frac{13}{30} = \frac{104}{30} \text{ bales per day}.
   \]

3. **Determine how long it takes for 8 cows to eat 17 bales of hay:**

   To find the number of days required for 8 cows to consume 17 bales of hay, divide the total amount of hay by the daily consumption of the 8 cows:
   \[
   \text{Days required} = \frac{17}{\frac{104}{30}} = \frac{17 \times 30}{104} = \frac{510}{104} \approx 4.9 \text{ days}.
   \]

### Final Answer:
It will take approximately **4.9 days** for 8 cows to eat 17 bales of hay.

Would you like further details or clarification?

Here are 5 related questions to consider:
1. How would the result change if the number of cows doubled?
2. What if the cows ate the hay at a variable rate instead of a constant rate?
3. How many bales of hay would 10 cows eat in 7 days at this rate?
4. If 3 cows joined after 2 days, how would that affect the time to finish the hay?
5. What would happen if the cows ate 15 bales of hay in 5 days instead of 13?

**Tip:** In work-rate problems, always find the rate for one unit (in this case, one cow) before scaling up or down!

Learn how to solve a work-rate problem where 6 cows eat 13 bales of hay in 5 days. This detailed solution explains the step-by-step approach to find out how long 8 cows will take to eat 17 bales of hay, covering key mathematical concepts like ratios and proportions. Suitable for students in Grades 6-8.

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