Five machines, five minutes, five widgets

Question

If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets? Answer quickly, then check the answer by working out how long a single machine takes to make a single widget. The two answers may not agree.

Accepted Answer

Five minutes. One machine, one widget. Five machines working together for 5 minutes produce 5 widgets, which means each machine produces one widget in 5 minutes. Scale up. A hundred machines each make one widget in 5 minutes, so together they make 100 widgets in 5 minutes. The number of machines and the number of widgets grew by the same factor, and the time per widget per machine never changed. Why 100 minutes is tempting. The three fives invite pattern-matching: "5, 5, 5, so 100, 100, 100". The instinct treats the problem as a proportion in which time scales with output, forgetting that cap…

Five machines, five minutes, five widgets

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