10 women complete a work in 7 days; 10 children complete the same work in 14 days. In how many days will 5 women and 10 children together complete the work?

Problem restatement
Combine the productivity of women and children using given group times, then compute the joint completion time.

Given data

• 10 women × 7 days = 1 job → woman's rate w satisfies 10w × 7 = 1 → w = 1/70.
• 10 children × 14 days = 1 job → child's rate c satisfies 10c × 14 = 1 → c = 1/140.

Concept/Approach
For 5 women and 10 children, add rates: 5w + 10c. Time = 1 ÷ (5w + 10c).

Step-by-step calculation
5w = 5 × (1/70) = 1/14 10c = 10 × (1/140) = 1/14 Combined rate = 1/14 + 1/14 = 1/7 job/day Time = 1 ÷ (1/7) = 7 days

Verification
Interpretation: 5 women produce as much per day as 10 children; together they double that to 1/7 per day.

Common pitfalls

• Incorrectly averaging days (7 and 14) rather than adding rates.

Final Answer
7 days