A works twice as fast as B. If B alone finishes the work in 12 days, in how many days will A and B together finish the work?

Problem restatementTwo workers have related speeds: A is twice as fast as B. Given B's solo time is 12 days, find the joint completion time for A and B.

Given data

• B's time = 12 days → B's rate = 1/12 job/day.
• A is twice as fast as B → A's rate = 2 × (1/12) = 1/6 job/day.

Concept/ApproachFor independent workers, rates add. Joint time = 1 ÷ (sum of rates).

Step-by-step calculation A's rate = 1/6 B's rate = 1/12 Combined rate = 1/6 + 1/12 = 1/4 job/day Joint time = 1 ÷ (1/4) = 4 days

Verification/AlternativeIn 4 days: A does 4 × 1/6 = 2/3; B does 4 × 1/12 = 1/3. Total = 1 job.

Common pitfalls

• Adding times (12 + 6) instead of adding rates.
• Misreading “twice as fast” as “twice the time.”

Final Answer4 days