5 men can build a 45 metre long wall in 9 days. How many men will build a 30 metre long wall in 5 days?

To solve this problem, we can use the concept of work done and proportionality. Here's the step-by-step process:

### Step 1: Calculate the work done by 1 man in 1 day
- **Given**: 5 men can build a 45-meter long wall in 9 days.
- **Total work**: \( 45 \) meters.

The work done by 5 men in 9 days:
\[
\text{Work done by 5 men in 9 days} = 45 \text{ meters}
\]

The work done by 1 man in 1 day:
\[
\text{Work done by 1 man in 1 day} = \frac{45 \text{ meters}}{5 \times 9 \text{ days}} = \frac{45}{45} = 1 \text{ meter per day}
\]

### Step 2: Calculate the total work required for the new task
- **New task**: Build a 30-meter long wall in 5 days.
- **Total work required**: 30 meters.

### Step 3: Calculate the number of men required
Let \( x \) be the number of men required to build a 30-meter long wall in 5 days.

The total work done by \( x \) men in 5 days:
\[
\text{Work done by } x \text{ men in 5 days} = x \times 1 \times 5 = 5x \text{ meters}
\]

Set this equal to the total work required (30 meters):
\[
5x = 30
\]

### Step 4: Solve for \( x \)
\[
x = \frac{30}{5} = 6
\]

### Conclusion:
To build a 30-meter long wall in 5 days, **6 men** are required.

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Would you like more details or have any questions?

Here are 5 related questions you might find interesting:
1. How many men are needed to build a 60-meter long wall in 10 days?
2. If the wall length is doubled, how many additional men are required?
3. What if 8 men were available—how many days would they take to build the 45-meter long wall?
4. How would the time change if only 4 men were available to build the 30-meter wall?
5. What is the relationship between the number of men and the days required for a fixed length?

**Tip:** When dealing with work problems, it's helpful to first calculate the work rate (e.g., work per person per day) and then use proportional reasoning to find the unknown.

Learn how to calculate the number of men needed to build a wall using proportional reasoning and work problem techniques. This problem involves determining how many men are required to build a 30-meter long wall in 5 days, based on the given information that 5 men can build a 45-meter wall in 9 days. Suitable for Grades 6-8.

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