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...

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?

jeew-m | Certified Educator

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.