10 men or 20 women or 30 children, can do a work in 15 days. If 10 men, 12 women and 18 children work on the same work, find the time in which work can be competed.
10 days
50/11 days
15 days
None of these

Let's define the work rate for each category of workers (men, women, and children) in terms of a single day of work.

### Step 1: Establish Work Rates
We know that:
- 10 men can complete the work in 15 days.
- 20 women can complete the work in 15 days.
- 30 children can complete the work in 15 days.

This means:
- 1 man can complete the work in \( 10 \times 15 = 150 \) days.
- 1 woman can complete the work in \( 20 \times 15 = 300 \) days.
- 1 child can complete the work in \( 30 \times 15 = 450 \) days.

### Step 2: Work Done Per Day by One Worker
- A man's daily work rate is \( \frac{1}{150} \) of the total work.
- A woman's daily work rate is \( \frac{1}{300} \) of the total work.
- A child's daily work rate is \( \frac{1}{450} \) of the total work.

### Step 3: Calculate Combined Work Rate
Now, let's calculate the combined work rate of 10 men, 12 women, and 18 children.

- Work done by 10 men in one day = \( 10 \times \frac{1}{150} = \frac{10}{150} = \frac{1}{15} \)
- Work done by 12 women in one day = \( 12 \times \frac{1}{300} = \frac{12}{300} = \frac{1}{25} \)
- Work done by 18 children in one day = \( 18 \times \frac{1}{450} = \frac{18}{450} = \frac{1}{25} \)

### Step 4: Total Work Done in One Day
The total work done in one day by 10 men, 12 women, and 18 children is:
\[
\frac{1}{15} + \frac{1}{25} + \frac{1}{25}
\]
Let's find the sum of these fractions:
\[
\frac{1}{15} + \frac{2}{25} = \frac{5}{75} + \frac{6}{75} = \frac{11}{75}
\]

### Step 5: Time to Complete the Work
The total work is done at the rate of \( \frac{11}{75} \) of the work per day. So, the time to complete the work is:
\[
\text{Time} = \frac{1}{\frac{11}{75}} = \frac{75}{11} \text{ days}
\]
This simplifies to approximately \( 6.82 \) days, which rounds to \( \frac{75}{11} \) days.

Thus, the correct answer is:
\[
\boxed{\frac{75}{11} \text{ days} = 50/11 \text{ days}}
\]

### Final Answer: **50/11 days**.

---

Do you need further clarification or details? Here are 5 related questions:

1. How would the answer change if there were 20 men instead of 10?
2. What would be the impact if the number of children doubled?
3. Can you derive a general formula for combining different types of workers to complete a task?
4. How much time would only 5 men and 5 women take to complete the task?
5. What is the individual contribution of a child compared to a man or a woman?

**Tip**: When solving work-rate problems, try to break them into manageable steps by calculating the rate for each worker per day.

10 men or 20 women or 30 children, can do a work in 15 days. If 10 men, 12 women and 18 children work on the same work, find the time in which work can be completed.
10 days
50/11 days
15 days
None of these

Solve a work and time problem involving 10 men, 12 women, and 18 children working together to complete a task. Explore the calculation of individual and combined work rates using formulas suitable for Grades 9-12. Final solution: 50/11 days.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation