3 jugs of water can fill 5/8 of a pail. Another jug and a cup of water are needed to fill the same remaining part of the pail. How many cups of water are needed to fill the same empty cup?

To solve this problem, let's break it down into steps:

1. **Determine the amount of water needed to fill the pail:**
   - 3 jugs of water fill \( \frac{5}{8} \) of the pail.
   - Therefore, 1 jug of water fills \( \frac{5}{8} \div 3 = \frac{5}{24} \) of the pail.

2. **Determine the remaining part of the pail to be filled:**
   - The remaining part of the pail that needs to be filled is \( 1 - \frac{5}{8} = \frac{3}{8} \).

3. **Determine the contribution of the additional jug and cup:**
   - According to the problem, another jug and a cup of water are needed to fill the remaining \( \frac{3}{8} \) of the pail.
   - Since 1 jug of water fills \( \frac{5}{24} \) of the pail, the remaining part to be filled by the cup is:
   \[
   \frac{3}{8} - \frac{5}{24} = \frac{9}{24} - \frac{5}{24} = \frac{4}{24} = \frac{1}{6}
   \]
   - Therefore, 1 cup of water fills \( \frac{1}{6} \) of the pail.

4. **Determine how many cups of water are needed to fill the pail:**
   - If 1 cup of water fills \( \frac{1}{6} \) of the pail, then to fill the entire pail:
   \[
   \text{Number of cups} = 1 \div \frac{1}{6} = 6 \text{ cups}
   \]

Therefore, **6 cups of water** are needed to fill the pail.

Would you like more details or have any questions?

Here are some related questions:

1. How do you convert between fractions of a container and units of volume?
2. How would the calculation change if one of the jugs was partially filled?
3. What if the pail had a different initial fraction filled, such as \( \frac{3}{4} \)?
4. How can you express the remaining volume of water needed in different units?
5. How would you calculate the volume of water in one jug if the total volume of the pail was given?
6. Can this problem be solved using a proportion instead of fractions?
7. How does the concept of unit rate apply to this problem?
8. What if you only had cups of water—how would you determine the number of cups needed from the beginning?

**Tip:** When working with fractions, always ensure they have a common denominator before performing any operations like addition or subtraction.

Learn how to solve a problem involving filling a pail using jugs and cups of water. Understand fractions and proportions in determining the amount of water needed. Suitable for high school students studying advanced fractions and volume concepts.

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