Master and apprentice: 12 and 24 days

A master alone can finish a batch of parts in 12 days, and an apprentice alone can finish the same batch in 24 days. Working together, how many days do they need?

Step-by-step

1. 1 ÷ 12 = 0.0833
   Work done per day by A
2. 1 ÷ 24 = 0.0417
   Work done per day by B
3. 1 ÷ (0.0833 + 0.0417) = 8
   Combined time = 1 ÷ combined rate

Why it works

Work rates add when two people work together, and each rate is 1 divided by that person's own time, so the shared time is 1 divided by the sum of the two rates.

Common mistakes

• Using the average of 12 and 24 days.
• Dividing by only the master's rate.

Related

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