If it would take Mark m hours to clean the house alone and with his brother Sam they can clean the house together in t hours. How many hours would it have taken Sam if he was working alone?

Question

Please explain this to me.

Answer 1

Answer 2

s represents time Sam needs working alone.

In t hours Mark does t / m of the work

In t hours Sam does t / s of the work

Together the do the one job

(t / m) + (t / s) = 1

st + mt = ms, multiply by LCD

mt = ms - st

mt = s(m - t)

mt / (m - t) = s