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If Machine A can complete a task in 6 hours and Machine B can complete the same task in 4 hours, how long will it take both machines working together to complete the task?

GRE · 2022 · quant slot 2
Question:
If Machine A can complete a task in 6 hours and Machine B can complete the same task in 4 hours, how long will it take both machines working together to complete the task?

Options

(A) 2 hours
(B) 2.4 hours
(C) 2.5 hours
(D) 3 hours
(E) 5 hours
Answer: (B) 2.4 hours

Explanation:
Machine A rate = 1/6 per hour, Machine B rate = 1/4 per hour. Combined rate = 1/6 + 1/4 = 2/12 + 3/12 = 5/12 per hour. Time = 1 ÷ (5/12) = 12/5 = 2.4 hours.

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