40 workers can dig 30 pits in 10 days, working 6 hours a day.
How many days will 20 workers take to dig 15 pits working 12 hours a day?


Let's break down the problem step by step.

### Step 1: Determine the total amount of work in terms of worker-hours.
We know that 40 workers can dig 30 pits in 10 days, working 6 hours per day. First, let's calculate the total worker-hours needed to dig these 30 pits.

\[
\text{Total worker-hours} = \text{Number of workers} \times \text{Number of days} \times \text{Hours per day}
\]
\[
\text{Total worker-hours} = 40 \times 10 \times 6 = 2400 \text{ worker-hours}
\]

These 2400 worker-hours are required to dig 30 pits.

### Step 2: Determine the worker-hours needed to dig 1 pit.
If 2400 worker-hours are needed to dig 30 pits, the worker-hours required for 1 pit are:

\[
\text{Worker-hours per pit} = \frac{2400 \text{ worker-hours}}{30 \text{ pits}} = 80 \text{ worker-hours per pit}
\]

### Step 3: Determine the total worker-hours required to dig 15 pits.
Now, calculate the total worker-hours needed to dig 15 pits:

\[
\text{Total worker-hours for 15 pits} = 80 \times 15 = 1200 \text{ worker-hours}
\]

### Step 4: Calculate the number of days needed for 20 workers working 12 hours a day.
The number of days \(D\) required can be found using the formula:

\[
\text{Total worker-hours} = \text{Number of workers} \times \text{Number of days} \times \text{Hours per day}
\]
\[
1200 = 20 \times D \times 12
\]

Solve for \(D\):

\[
1200 = 240D
\]
\[
D = \frac{1200}{240} = 5 \text{ days}
\]

### Final Answer:
So, 20 workers will take **5 days** to dig 15 pits working 12 hours a day.

Would you like more details or have any further questions? Here are some related questions:

1. How would the number of days change if only 10 workers were available?
2. What if the workers worked 8 hours a day instead of 12 hours?
3. How can you calculate the number of workers needed to finish a job in a certain number of days?
4. Can you apply this method to other similar problems involving different tasks?
5. How would the problem change if the efficiency of workers varied over time?

**Tip:** Always start by calculating the total amount of work required and then relate it to the available resources (workers, hours, days) to find the solution efficiently.

Learn how to solve a work and time problem involving 20 workers digging 15 pits in 12 hours a day. Follow step-by-step calculations and understand the application of the work formula. Suitable for Grades 7-9 students learning arithmetic and problem-solving techniques.

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