Question 1012955
To complete a work 'A' takes 50% more time than 'B'.
 If together they take 18 days to complete the work, how much time will 'B' take to do it? 
:
let b = time required by B to do the job
"To complete a work 'A' takes 50% more time than 'B'"; therefore
1.5b = Time required by A to do the job
:
Let the completed job = 1
Each will do a fraction of the job, the two fractions add up to 1
{{{18/(1.5b)}}} + {{{18/b}}} = 1
Get rid of the fractions, multiply equation by 3b
3b*{{{18/(1.5b)}}} + 3b*{{{18/b}}} = 3b(1)
Cancel the denominators
2(18) + 3(18) = 3b
36 + 54 = 3b
90 = 3b
b = 90/3
b = 30 hrs required by B to do the job alone
:
:
Check this
{{{18/(1.5*30)}}} + {{{18/30}}} = 1
{{{18/45}}} + {{{18/30}}} = 1
using a calc
.4 + .6 = 1