Two machines, working together, take 2hours 24minutes to complete a job. Working on its own, one machine takes 2 hours longer than the other to complete the job. How long does the slower machine take on its own?
Let us say the amount of work to be done is X.
If machine one takes t hrs to finish the job then machine two will take (t+2) hrs.
Work rate of machine one `= X/t`
Work rate of machine two `= X/(t+2)`
When both operating the job will be done in 2.4 hrs.( 2 hrs and 24 min.)
`Work = (Rate)xx(Time)`
`X = X/txx2.4+X/(t+2)xx2.4`
`t(t+2) = 2.4(t+t+2)`
`t^2+2t-4.8t-4.8 = 0`
`t^2-2.8t-4.8 = 0`
Solving this by quadratic equation will give you;
`t = ((-2.8)+-sqrt((-2.8)^2-4xx1xx(-4.8)))/(2xx1)`
`t = 4 ` OR `t = -1.2`
Since time cannot be negative t = 4.
So the faster machine will take 4 hrs to complete the job and slower machine will take (4+2) = 6 hrs to complete the job.