Mo2men 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 job = the LCM of 10, 4 and 5 = 20 widgets.
Since A takes 10 hours to produce 20 widgets, A's rate = w/t = 20/10 = 2 widgets per hour.
Since B takes 4 hours to produce 20 widgets, B's rate = w/t = 20/4 = 5 widgets per hour.
Since C takes 5 hours to produce 20 widgets, C's rate = w/t = 20/5 = 4 widgets per hour.
Combined rate for A+B+C = 2+5+4 = 11 widgets per hour.
After A, B and C work together for an hour to produce 11 widgets, the remaining work = 20-11 = 9 widgets.
Since C's rate = 4 widgets per hour, the time for C to produce the remaining 9 widgets = w/r = 9/4 hours.
The correct answer is
B.
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