A, B, C can complete a work in 24, 6, and 12 days respectively. Working together, how long will they take to complete the work?

Problem restatementCombine individual rates of A, B, and C to get a joint completion time.

Given data

• A's time = 24 days → rate = 1/24.
• B's time = 6 days → rate = 1/6.
• C's time = 12 days → rate = 1/12.

Concept/ApproachIndependent workers' rates add: joint rate = 1/24 + 1/6 + 1/12.

Step-by-step calculation Joint rate = 1/24 + 1/6 + 1/12 = 1/24 + 4/24 + 2/24 = 7/24 job/day Joint time = 1 ÷ (7/24) = 24/7 days 24/7 days ≈ 3.4286 days ≈ 3 days 10 hours 17 minutes

VerificationIn 24/7 days, total work = (7/24) × (24/7) = 1 (exact).

Common pitfalls

• Taking average of times (24, 6, 12) rather than adding rates.

Final Answer24/7 days (≈ 3 days 10 hours)