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Working together at their respective constant rates, machine R, machine S, and machine T can produce a batch of parts in 4 hours. If machine R, working alone at its constant rate, can produce the same batch of parts in 6 hours, how many hours would it take machine S and machine T, working together at their respective constant rates, to produce the same batch of parts?
  • a)
    6
  • b)
    8
  • c)
    10
  • d)
    12
  • e)
    14
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Working together at their respective constant rates, machine R, machin...
Assuming the rates of machines R, S, and T are r, s, and t, respectively, we are given:
  • r + s + t = 1/4 and r = 1/6.
Subtracting the second equation from the first results in:
  • s + t = 1 = 1/4 - 1/6 = 1/12.
Since rate is the reciprocal of time, machine S and machine T, would take 12 hours to produce the same batch of parts.
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Working together at their respective constant rates, machine R, machine S, and machine T can produce a batch of parts in 4 hours. If machine R, working alone at its constant rate, can produce the same batch of parts in 6 hours, how many hours would it take machine S and machine T, working together at their respective constant rates, to produce the same batch of parts?a)6b)8c)10d)12e)14Correct answer is option 'D'. Can you explain this answer?
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