Mixed workforce (men and women): 3 men can finish a job in 6 days and 5 women can finish the same job in 18 days. If 4 men and 10 women work together, how many days will they require to finish the job?

Introduction / Context:
We combine different worker categories with different efficiencies. Convert both groups into daily rates from their solo completion info, add the rates for the mixed team, and then invert to get total days needed.

Given Data / Assumptions:

• 3 men in 6 days ⇒ 3m * 6 = 1 ⇒ m = 1/18 job/day.
• 5 women in 18 days ⇒ 5w * 18 = 1 ⇒ w = 1/90 job/day.
• Team = 4 men + 10 women.

Concept / Approach:
Team rate = 4m + 10w. Then days = 1 / (team rate). Each rate is constant and additive since they work simultaneously on the same job.

Step-by-Step Solution:
m = 1/18; w = 1/90. Team rate = 4*(1/18) + 10*(1/90) = 4/18 + 10/90 = 2/9 + 1/9 = 1/3. Days = 1 / (1/3) = 3 days.

Verification / Alternative check:
Note that 1 man = 5 women in productivity (since 1/18 : 1/90 = 5:1). The team equals 4 men + 10 women = 4 + 2 man-equivalents = 6 men ⇒ 6 men at 1/18 each give 6/18 = 1/3 job/day ⇒ 3 days.

Why Other Options Are Wrong:
2, 4, or 5 days contradict the calculated combined rate.

Common Pitfalls:
Averaging days instead of rates; you must convert to daily rates before summing across categories.

Final Answer:
3 days