fortytwo men can compleate a work in 15 days how many days it will take to complete the same work for 30 members

To solve this, we use the concept of **man-days**, which means that the total amount of work done is the same, regardless of how many workers are involved, as long as the total man-days are the same.

The total amount of work is:

\[
\text{Work} = \text{Number of men} \times \text{Number of days}
\]

For the first case, the total work can be expressed as:

\[
\text{Work} = 42 \text{ men} \times 15 \text{ days} = 630 \text{ man-days}
\]

Now, we want to find how many days it will take for 30 men to complete the same work. Let \(x\) be the number of days for 30 men:

\[
\text{Work} = 30 \text{ men} \times x \text{ days} = 630 \text{ man-days}
\]

Now solve for \(x\):

\[
30x = 630
\]

\[
x = \frac{630}{30} = 21 \text{ days}
\]

Thus, it will take **21 days** for 30 men to complete the same work.

Would you like further details on this or have any other questions?

Here are 5 related questions:
1. If 42 men took 10 days to complete the work, how long would 28 men take?
2. If 15 men can complete a work in 20 days, how many men are needed to finish it in 10 days?
3. If 30 men can complete a work in 21 days, how long would 60 men take to complete the same work?
4. What if 42 men work for half a day every day? How many days would it take to finish the work?
5. How would the completion time change if one worker becomes twice as efficient?

**Tip:** Always check the proportion of workers and days in such problems; they are inversely related!

Solve the work and time problem: If 42 men can complete a task in 15 days, how long will it take for 30 men? Learn the concept of man-days, inverse proportion, and get a detailed step-by-step solution. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation