Problem Solving

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) 7

1) 6 machines complete a job in 12 days.
translates to 6 machines do 1/12 job in 1 day.

2) so 1 machine is 1/6M does 1/12J in 1 day.

using rate * distance = time

1/6M * 1/12J = 1/72MJ

3) To translate how many machines are required in 8 days:
each machine would have to 1/8J

such that 1/72 MJ / 1/8J = 1/9M 9 machines are required

9 - 6 = 3 additional machines