Question
It takes 21 hours for 12 men to resurface a
stretch of road. Find how many men it takesto
resurface a similar stretch of road in 50 hours
24 minutes, assuming the work rate remains
constan
stretch of road. Find how many men it takesto
resurface a similar stretch of road in 50 hours
24 minutes, assuming the work rate remains
constan
Answers
GPT-4o mini
To solve the problem, we first need to find the total amount of work done in "man-hours" by the original group of men.
1. Calculate the total work done in man-hours:
- 12 men work for 21 hours.
- Total work = Number of men × Time = 12 men × 21 hours = 252 man-hours.
2. Convert 50 hours 24 minutes into hours:
- 24 minutes = 24/60 hours = 0.4 hours.
- Total time = 50 hours + 0.4 hours = 50.4 hours.
3. Let \( x \) be the number of men required to complete the work in 50.4 hours. The work required remains the same (252 man-hours).
- So, we set up the equation:
\[
x \times 50.4 = 252
\]
4. Solve for \( x \):
\[
x = \frac{252}{50.4} \approx 5
\]
Therefore, it takes **5 men** to resurface a similar stretch of road in 50 hours and 24 minutes.
1. Calculate the total work done in man-hours:
- 12 men work for 21 hours.
- Total work = Number of men × Time = 12 men × 21 hours = 252 man-hours.
2. Convert 50 hours 24 minutes into hours:
- 24 minutes = 24/60 hours = 0.4 hours.
- Total time = 50 hours + 0.4 hours = 50.4 hours.
3. Let \( x \) be the number of men required to complete the work in 50.4 hours. The work required remains the same (252 man-hours).
- So, we set up the equation:
\[
x \times 50.4 = 252
\]
4. Solve for \( x \):
\[
x = \frac{252}{50.4} \approx 5
\]
Therefore, it takes **5 men** to resurface a similar stretch of road in 50 hours and 24 minutes.