Six machines, each working at the same constant rate

Six machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 8 days?
A. 2
B. 3
C. 4
D. 6
E. 8

Say a single machine requires x days to complete the job. Hence, the rate of one machine is 1/x job/day, (as the rate is reciprocal of time). Consequently, the combined rate for six machines is 6/x.

Using the equation 'work = time*rate', we have 1 = 12*6/x, which simplifies to x = 72 days. Therefore, a single machine would take 72 days to complete the task.

To finish the task in 8 days, 72/8 = 9 machines are needed.

The difference is thus 9 - 6 = 3 machines.

Answer: B.

Alternatively, we can consider it like this: we want to reduce the completion time from 12 days to 8, which is 2/3 of the original time. Consequently, we need to increase the work rate to 3/2 of the original rate. This implies we need 6*3/2 = 9 machines in total. Therefore, an additional 3 machines are required.