If 5 men can dig 18 metres ditch in 12 hours, in how many hours will 15 men working at the same rate dig 27 metres ditch?

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UpStudy AI · Accepted Answer

To solve this problem, we'll use the concept of **man-hours**, which combines the number of workers and the time they spend working.

1. **Calculate the Total Man-Hours for the First Scenario:**
   
   - **Number of men:** 5
   - **Time:** 12 hours
   - **Total man-hours:** $$5 \text{ men} \times 12 \text{ hours} = 60 \text{ man-hours}$$
   
   These 60 man-hours allow the team to dig 18 meters of ditch.

2. **Determine the Work Rate:**
   
   - **Work done per man-hour:** $$\frac{18 \text{ meters}}{60 \text{ man-hours}} = 0.3 \text{ meters per man-hour}$$

3. **Calculate the Required Man-Hours for the Second Scenario:**
   
   - **Desired ditch length:** 27 meters
   - **Total man-hours needed:** $$\frac{27 \text{ meters}}{0.3 \text{ meters per man-hour}} = 90 \text{ man-hours}$$

4. **Determine the Time Needed with 15 Men:**
   
   - **Number of men:** 15
   - **Total man-hours needed:** 90
   
   $$
   \text{Time} = \frac{\text{Total man-hours}}{\text{Number of men}} = \frac{90}{15} = 6 \text{ hours}
   $$

**Answer:**  
6 hours.
It will take 6 hours for 15 men to dig a 27-meter ditch.

If 5 men can dig 18 metres ditch in 12 hours, in how many hours will 15 men working at the same rate dig 27 metres ditch?

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