Mother–Daughter Team vs. Mother Alone A woman can weave a basket in 6 days. With the help of her daughter, they finish in 4 days. How long would the daughter alone take to weave the basket?

Introduction / Context:
This is a basic “helper” problem: compare the solo time of one worker to the combined time with a helper, then solve for the helper’s solo time via rate subtraction.

Given Data / Assumptions:

• Woman alone: 6 days ⇒ 1/6 per day.
• Together: 4 days ⇒ 1/4 per day.
• Rates add linearly.

Concept / Approach:
Daughter’s rate = together rate − mother’s rate = 1/4 − 1/6. Daughter’s time = reciprocal of her rate.

Step-by-Step Solution:
Daughter rate = 1/4 − 1/6 = (3 − 2)/12 = 1/12 per day.Daughter alone time = 1 / (1/12) = 12 days.

Verification / Alternative check:
Check: 1/6 + 1/12 = 1/4; correct combined rate.

Why Other Options Are Wrong:
16, 10, 8, or 14 days do not match the calculated helper rate.

Common Pitfalls:
Subtracting times instead of rates; remember to subtract 1/6 from 1/4, not 6 from 4.

Final Answer:
12 days