It's usually helpful with these problems to determine the rate of each machine.

All six machines take 12 days to do this job. If it were just one machine working at the job, it would take six times as long to finish the job, or 72 days.

If the job is to be completed in 8 days, then 72/8 = 9 machines to get the job done. This means 3 additional machines.

IMO B. 3.

Here it goes..

6 machines 1 day work = 1/12
therefore 1 machines 1 day work is 1/72

therefore that total number of machines required if we have a constraint on number of days (8) is 72/8 = 9 machines

hence the additional machiney is 9-6 ( we already have) = 3.

Hope it helps..

6 mach = 12 days

therefore, 6 mach = 1/12 work / day...(1)


Let x be the number of additional machines required to do d work in 8 days.

so , (6+x)mach = 1/8 work / day ...(2)

cross multiply 1 and 2 to get x


thus, ( 6 + x) 1/12 = 6 / 8

thus x=3

Thanks guys for the help. Made me understand it for sure. Hopefully I get one of these in 10 days my math score is improving vastly, but I want to get my errors to so gle digits.. I got 13 today!! Close but no cigar!!