Men–women–children equivalence and a family crew Either 4 men or 6 women or 10 children can paint a house in 5 days. A couple (1 man + 1 woman) and their 5 sons (children) are hired. In how many days will they finish the job?

Introduction / Context:
When different groups can complete a job in the same time, we can infer equivalent individual rates. Once we know the man, woman, and child rates, we sum the family’s daily rate and invert to get total time.

Given Data / Assumptions:

• 4 men in 5 days ⇒ 1 job.
• 6 women in 5 days ⇒ 1 job.
• 10 children in 5 days ⇒ 1 job.
• Crew used: 1 man + 1 woman + 5 children.

Concept / Approach:
Let the job be 1 unit. Compute per-day per-person rates from the equivalences, then sum the family’s rates.

Step-by-Step Solution:

Verification / Alternative check:
Check partial: In 5 days, they would do 5 * 11/60 = 11/12 of the job, leaving 1/12; another 1/ (11/60) − 5 ≈ 0.45 day finishes it.

Why Other Options Are Wrong:
56/11 ≈ 5.09, 11/2 = 5.5, and 6 are not the exact reciprocal of 11/60.

Common Pitfalls:
Forgetting that “4 men in 5 days” implies a single man-day rate of 1/20.

Final Answer:
60/11 days