Question
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?
Ask by Chan Conner. in Nigeria
Jan 13,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
It will take 6 hours for 15 men to dig a 27-meter ditch.
Solution
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.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Bonus Knowledge
To solve the problem, first, we find the work rate of the 5 men. They dig 18 meters in 12 hours, so their rate is: Rate = 18 meters / 12 hours = 1.5 meters per hour for 5 men. Now, for 1 man, it would be: Rate per man = 1.5 meters/hour / 5 = 0.3 meters/hour. Next, we calculate the rate for 15 men: Rate for 15 men = 0.3 meters/hour * 15 = 4.5 meters/hour. Now, to dig a 27 meters ditch, the time required can be calculated as: Time = Distance / Rate = 27 meters / 4.5 meters/hour = 6 hours. So, 15 men working at the same rate will dig a 27-meter ditch in 6 hours. Hope that helps!
