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?
Correct Answer: 33/7 days
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