lheiannie07 wrote:Machine A can do a job in 24 hours at a constant rate. If Machine A does the job for 8 hours and Machine B does the rest of the job, which works at 2/3 constant rate of Machine A. How long will it take for Machine B alone to do the rest of the job?
A. 12hrs
B. 16hrs
C. 24hrs
D. 28hrs
E. 32hrs
Let the job = 72 widgets.
Since A takes 24 hours to complete the job, A's rate = w/t = 72/24 = 3 widgets per hour.
At a rate of 3 widgets per hour, the work produced by A in 8 hours = rt = 3*8 = 24 widgets.
Remaining work = 72-24 = 48 widgets.
Since B's rate is 2/3 of A's rate, B's rate = (2/3)(3) = 2 widgets per hour.
At a rate of 2 widgets per hour, the time for B to produce the remaining 48 widgets = w/r = 48/2 = 24 hours.
The correct answer is
C.
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