6 builders can build 10 houses in 30 months. How long would it take for 18 builders to build 10 houses

To determine how long it would take for 18 builders to build 10 houses, we first need to find the rate at which the builders are working. Let's break down the given information and calculate the time needed.

First, calculate the rate at which 6 builders build the houses.

\[
\text{Rate of 6 builders} = \frac{10 \text{ houses}}{30 \text{ months}} = \frac{1 \text{ house}}{3 \text{ months}}
\]

This means that 6 builders can build 1 house in 3 months. To find the rate per builder, divide by 6:

\[
\text{Rate per builder} = \frac{1 \text{ house}}{3 \text{ months} \times 6 \text{ builders}} = \frac{1 \text{ house}}{18 \text{ months}}
\]

So, 1 builder can build 1 house in 18 months.

Now, if we have 18 builders, we need to calculate their combined rate. Since each builder works independently, the combined rate of 18 builders is 18 times the rate of 1 builder:

\[
\text{Rate of 18 builders} = 18 \times \frac{1 \text{ house}}{18 \text{ months}} = \frac{18 \text{ houses}}{18 \text{ months}} = \frac{1 \text{ house}}{1 \text{ month}}
\]

Therefore, 18 builders can build 1 house in 1 month. To find out how long it takes them to build 10 houses:

\[
\text{Time to build 10 houses} = 10 \times \frac{1 \text{ month}}{1 \text{ house}} = 10 \text{ months}
\]

So, it would take 18 builders 10 months to build 10 houses.

Do you want details or have any questions?

Here are some questions you might ask:
1. How does the calculation change if the number of houses changes?
2. What if the builders work at different rates?
3. How can we adjust for part-time builders?
4. What if there are breaks or delays in the building process?
5. Can we apply this calculation to different types of projects?

**Tip:** Always break down the given information into manageable parts and solve step-by-step to avoid errors.

Explore how to calculate the time required for builders to construct houses based on their working rates. This problem involves proportional reasoning and unit rate calculations. Suitable for high school students studying proportional relationships and rates of work.

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