Determine a woman’s solo time from a mixed team: 10 men and 15 women finish a work in 6 days. One man alone can finish the same work in 100 days. In how many days can one woman alone finish the work?

Introduction / Context:
We are given the team time and one man’s solo time. From the team rate equation, we can isolate the woman’s rate and then invert to find her solo completion time. This is a straightforward linear rate problem once written correctly.

Given Data / Assumptions:

• Total job = 1.
• 1 man’s time = 100 days ⇒ man’s rate m = 1/100.
• (10 men + 15 women) complete in 6 days ⇒ team rate = 1/6.

Concept / Approach:
Team rate = 10m + 15w = 1/6. Substitute m = 1/100 and solve for w (woman’s rate). Then woman’s solo time is 1 / w days.

Step-by-Step Solution:
10m + 15w = 1/6 ⇒ 10*(1/100) + 15w = 1/6. 0.1 + 15w = 0.166666... ⇒ 15w = 0.066666... = 1/15. Therefore, w = (1/15)/15 = 1/225. One woman’s time = 1 / (1/225) = 225 days.

Verification / Alternative check:
Plugging back: 10*(1/100) + 15*(1/225) = 0.1 + 0.066666... = 0.166666... = 1/6, consistent.

Why Other Options Are Wrong:
125, 150, 90 days do not satisfy the team equation when substituted.

Common Pitfalls:
Rounding errors with repeating decimals; treat 1/6 exactly when possible to avoid drift.

Final Answer:
225 days