Question 112660
Jim can fill the pool in 30 minutes 


So in one minute he can fill {{{1/30}}} of the tank


Sue can fill the same pool in 45  minutes.


So in one minute she can fill {{{1/45}}} of the tank


Tony can fill the pool in 90 minutes.


So in one minute he can fill {{{1/90}}} of the tank


so the time taken by all of them to fill the same pool is given by:


{{{(1/30) + (1/45) + (1/90)}}} 


{{{(3 + 2 + 1)/90}}}    taking LCM we get this:



{{{(6/90)}}}


==> {{{(1/15)}}}


so taking reciprocal we get the time taken by all the three to fill the tank


==> they take 15 minutes in total to fill the tank.


Hence the solution.