Question 297627
The way I like to do these is to look at each one's daily rate. Then add their daily rate to see how they can work together.

So Sam can do 1/3 of the job in a day (so he takes 3 days to do the job alone)
John can do 1/5 of the job in a day (it take him 5 days to do the whole thing)
Together, their daily rate is {{{1/3 + 1/5}}} = {{{5/15 + 3/15}}} = {{{8/15}}}
So they can do over half the job in a ay
To do the whole job
{{{rate*time = WorkDone}}}
{{{(8/15) * time = 1}}} 1 job is a whole job done once
{{{time = 15/8}}}
So working together they can do the job in 1 and 7/8's days.

Make sense now?