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Three machines, A, B, and C, can complete a certain task

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Three machines, A, B, and C, can complete a certain task

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Three machines, A, B, and C, can complete a certain task in 10 hours, 4 hours, and 5 hours respectively. If all 3 machines worked together for 1 hour and then stop, how many hours does it take machine C to complete the job?

A. 4/5
B. 9/4
C. 11/4
D. 4
E. 13/2

The OA is B.

What is the equation that helps me to solve this DS question? I need your help experts. Thanks.

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VJesus12 wrote:
Three machines, A, B, and C, can complete a certain task in 10 hours, 4 hours, and 5 hours respectively. If all 3 machines worked together for 1 hour and then stop, how many hours does it take machine C to complete the job?

A. 4/5
B. 9/4
C. 11/4
D. 4
E. 13/2
Let the task = the LCM of 10, 4 and 5 = 20 units.
Since A takes 10 hours to complete the 20-unit task, A's rate = w/t = 20/10 = 2 units per hour.
Since B takes 4 hours to complete the 20-unit task, B's rate = w/t = 20/4 = 5 units per hour.
Since C takes 5 hours to complete the 20-unit task, C's rate = w/t = 20/5 = 4 units per hour.
Since the combined rate for A+B+C = 2+5+4 = 11 units per hour, the amount of work produced by the 3 machines in 1 hour = 11 units.
Since C's rate = 4 units per hour, the time for C to produce the remaining 9 units = w/r = 9/4 hours.

The correct answer is B.

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