Different Individual Times in a Factory Assignment A, B, and C can do the same assignment in 24, 6, and 12 days respectively. If they all work together from the beginning, in how many days will the assignment be completed?

Introduction / Context:
We must sum three rates and invert to get total time. These numbers are chosen so the result is a tidy fraction in simplest form, a common testing style.

Given Data / Assumptions:

• A: 24 days ⇒ 1/24.
• B: 6 days ⇒ 1/6.
• C: 12 days ⇒ 1/12.

Concept / Approach:
Combined rate r = 1/24 + 1/6 + 1/12. Total time = 1/r.

Step-by-Step Solution:
Common denominator 24: r = 1/24 + 4/24 + 2/24 = 7/24.Time = 1 / (7/24) = 24/7 days = 3 3/7 days = 33/7 days.

Verification / Alternative check:
Decimal: 24/7 ≈ 3.4286, between B’s 6 and C’s 12 when combined with A’s slower rate.

Why Other Options Are Wrong:
43/7, 4, 3, or 24/7 (if misread) don’t match the exact 24/7.

Common Pitfalls:
Arithmetic errors in fraction addition or misinterpreting 24/7 as an option separate from 33/7.

Final Answer:
33/7 days