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Machine A can complete a job in 6 hours, and Machine B can complete the same job in 4 hours. Working together, how long will it take them to complete the job?

GRE · 2023 · quant slot 2
Question:
Machine A can complete a job in 6 hours, and Machine B can complete the same job in 4 hours. Working together, how long will it take them to complete the job?

Options

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

Explanation:
Rate of A = 1/6 jobs/hour. Rate of B = 1/4 jobs/hour. Combined rate = 1/6 + 1/4 = 2/12 + 3/12 = 5/12 jobs/hour. Time = 1 job ÷ (5/12 jobs/hour) = 12/5 = 2.4 hours.

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