Question 150565
Let {{{r}}}= Roma's rate of working
Let {{{a}}}= Amor's rate of working
{{{r + a = t}}}, their rate working together
Roma's rate is (1 garden weeded)/4.5 hrs
{{{1/4.5 + a = t}}}
What part of the job did Roma do in 2 hours?
{{{(1/4.5)*2 = 4/9}}}
So, {{{5/9}}} of the job is left when Amor joins her
They did {{{5/9}}} of the job in {{{2}}} hrs
{{{(5/9)/2}}} is their rate working together
Multiply top and bottom by {{{9/5}}}
{{{((9/5)/(9/5))*((5/9)/2) = 1/(18/5)}}}
They can do the whole job in {{{18/5}}} of an hour
{{{(18/5)*60}}} = 3 hrs 36 min answer
-------
To find Amor's time to do the whole job,
{{{1/4.5 + a = t}}}
{{{2/9 + a = 5/18}}}
Multiply both sides by {{{18}}}
{{{4 + 18a = 5}}}
{{{18a = 1}}}
{{{a = 1/18}}} This is Amor's rate, which is
(1 job)/(18 hours)
It takes Amor {{{18}}} hrs to do the job alone