M7MBA 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.
In 1 hour, the work produced by A+B+C = 2+5+4 = 11 units.
Remaining work = 20-11 = 9 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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