Sure! Let's walk through solving this problem step-by-step.
1. Understand the Problem:
- We have 20 people who can complete a certain amount of work in 3 days.
- We need to determine how many people are needed to complete the same amount of work in 2 days.
2. Total Work Calculation:
- The total amount of work can be thought of in "person-days," meaning how much work one person could do in one day.
- With 20 people working for 3 days, the total amount of work is:
[tex]\[
\text{Total work} = 20 \text{ people} \times 3 \text{ days} = 60 \text{ person-days}
\][/tex]
3. Determine People Required for 2 Days:
- If we want to complete 60 person-days of work in 2 days, we need to find the number of people required.
- Let [tex]\( P \)[/tex] represent the number of people needed to complete this work in 2 days. The total work would then be:
[tex]\[
\text{Total work} = P \text{ people} \times 2 \text{ days} = 60 \text{ person-days}
\][/tex]
4. Solve for [tex]\( P \)[/tex]:
- Rearranging the equation to solve for [tex]\( P \)[/tex]:
[tex]\[
P = \frac{60 \text{ person-days}}{2 \text{ days}} = 30 \text{ people}
\][/tex]
5. Conclusion:
- Therefore, to complete the same amount of work in 2 days, you would need 30 people.
Hence, the number of people required to complete the work in 2 days is 30.
