To solve the problem, we first need to find the total amount of work done in "man-hours" by the original group of men.
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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.
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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.
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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: \[ x \times 50.4 = 252 \]
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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.