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If 4 men can build a wall in 6 hours, how long will it take 8 men working at the same rate?

Answer

It will take 3 hours. The total work is $4 \times 6 = 24$ man-hours, and with 8 men the time is $24 \div 8 = 3$ hours.

Explanation

What the problem is really asking

When workers all have the same rate, the time to finish a fixed job changes inversely with the number of workers. More men means fewer hours for the same wall.

Convert the job into “man-hours”

Think of the wall as a fixed amount of work.

Total work: $$ \text{Work} = 4\text{ men} \times 6\text{ hours} = 24\text{ man-hours} $$

Find the new time with 8 men

If 8 men do the same total work of 24 man-hours, then $$ \text{Time} = \frac{24\text{ man-hours}}{8\text{ men}} = 3\text{ hours} $$

Quick check (does it make sense?)

Doubling the number of men from 4 to 8 should cut the time in half, and $6/2 = 3$, so the result is consistent.

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