Help solving what should be an easy and quick problem

gen3hatch wrote: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 need to complete the job in 8 days?
A 2
B 3
C 4
D 6
E 8

Can you show the work and calculations behind the answer?

Hi,

if all 6 machines work at the same rate, then it takes 6*12 = 72 machine days to complete the job.

If we want to complete the job in 8 days, we simply calculate:

(amount of work to do job)/(# of days to complete) = 72 machine days/8 days = 9 machines

We already have 6 machines, so we need 9-6 = 3 more machines: choose B.

* * *

What we basically did was set up the equation:

6*12 = x*8

and solved for x to get the total number of machines.

Wow you made that seem too easy...I knew there was an easy solution but I kept making it too complicated...Thanks

IMO B. this is inverse relationship, the more machines the less days. So, 12/8 = x/6 -----------> x= 9 machines to finish the job in 8 days. Already have 6 machines, so we need 3 more.