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. <i class="em em-disappointed"></i>
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Three machines, A, B, and C, can complete a certain task
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Let the task = the LCM of 10, 4 and 5 = 20 units.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
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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The combined rate of A, B, and C is: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
1/10 + 1/4 + 1/5 = 2/20 + 5/20 + 4/20 = 11/20. So if all the machines work for 1 hour, 11/20 of the job is completed, and 9/20 is left to be completed.
Thus, it would take machine C (9/20)/(1/5) = 45/20 = 9/4 hours to complete the job.
Answer: B
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