if 5 men can construct2 corttages in 21 days how many more men working at the same rate will be needed to construct 6 cottages in the same period

To solve this problem, let's break it down step by step:

1. **Determine the rate of construction for one man:**
   - 5 men can construct 2 cottages in 21 days.
   - Therefore, the number of cottages constructed by 1 man in 21 days is:
     \[
     \frac{2}{5} \text{ cottages}
     \]

2. **Determine the rate of construction per day for one man:**
   - The number of cottages constructed by 1 man in 1 day is:
     \[
     \frac{2}{5 \times 21} = \frac{2}{105} \text{ cottages/day}
     \]

3. **Determine the number of men needed to construct 6 cottages in 21 days:**
   - The total number of cottages needed is 6.
   - The total number of days available is 21.
   - Therefore, the number of cottages needed per day is:
     \[
     \frac{6}{21} = \frac{2}{7} \text{ cottages/day}
     \]

4. **Determine the number of men required to meet this daily construction rate:**
   - Let \( n \) be the number of men required.
   - Each man constructs \(\frac{2}{105} \text{ cottages/day}\).
   - Therefore, we need:
     \[
     n \times \frac{2}{105} = \frac{2}{7}
     \]
   - Solving for \( n \):
     \[
     n = \frac{\frac{2}{7}}{\frac{2}{105}} = \frac{2}{7} \times \frac{105}{2} = 15
     \]

5. **Calculate the additional men needed:**
   - Initially, there were 5 men.
   - Therefore, the additional men required are:
     \[
     15 - 5 = 10
     \]

So, **10 more men** working at the same rate will be needed to construct 6 cottages in the same period.

Would you like details or have any questions?

Here are 8 related questions to expand on this information:

1. How many men are needed to construct 4 cottages in 21 days?
2. If the number of men is doubled, how many cottages can be constructed in 21 days?
3. How many days would it take for 5 men to construct 6 cottages?
4. How many cottages can 10 men construct in 21 days?
5. If the construction rate doubles, how many men are needed to construct 6 cottages in 21 days?
6. How many cottages can be constructed by 3 men in 21 days?
7. If 8 men can construct 3 cottages in 21 days, how many days will it take 8 men to construct 6 cottages?
8. How many cottages can be constructed in 21 days by \( n \) men?

**Tip:** When dealing with rates and work problems, use the concept of work per unit time and then scale up or down based on the total work required.

Explore a detailed solution to a construction rate problem involving men working together to build cottages. Learn how to calculate the additional men required to construct 6 cottages in 21 days based on given rates of work. Suitable for Grades 7-9.

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