To determine how many men are required to construct a 60-meter long wall in 24 days, let's break it down step-by-step.
### Step 1: Determine the Work Rate
First, note that 20 men can construct an 80-meter long wall in 8 days. We need to find the work rate in terms of man-days per meter.
1. Total man-days for the original task:
- 20 men working for 8 days equals 20 * 8 = 160 man-days.
2. Work rate per meter:
- Since 160 man-days are required to build 80 meters, the work rate is:
[tex]\[
\text{Work Rate} = \frac{160 \text{ man-days}}{80 \text{ meters}} = 2 \text{ man-days per meter}
\][/tex]
### Step 2: Calculate Total Effort Needed for 60 Meters
We need to find out how many man-days are required to build a 60-meter long wall:
1. Total effort needed:
- Given the work rate of 2 man-days per meter, for 60 meters, the total effort needed is:
[tex]\[
60 \text{ meters} \times 2 \text{ man-days per meter} = 120 \text{ man-days}
\][/tex]
### Step 3: Determine the Number of Men Required
Lastly, we need to find out how many men are required to complete 120 man-days of work in 24 days.
1. Number of men required:
- To find the number of men required, divide the total man-days by the number of days:
[tex]\[
\frac{120 \text{ man-days}}{24 \text{ days}} = 5 \text{ men}
\][/tex]
### Conclusion
To construct a 60-meter long wall in 24 days, you will need 5 men.
