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?
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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.
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