Question 373417
Let {{{r}}} = the apprentices rate of working
Then {{{2r}}} = the experienced bricklayer's rate of working
If I add their rates and multiply by hours worked, that
will give me the fraction of the job completed
When the experienced bricklayer quit, that fraction is
{{{(r + 2r)*12}}}
Now the remaining fraction of the job is done in 12 hours
That fraction is {{{r*12 }}}
Now I can say
{{{3r*12 = 1 - r*12}}}
{{{36r = 1 - 12r}}}
{{{48r = 1}}}
{{{r = 1/48}}}
{{{2r = 2/48}}}
{{{2r = 1/24}}}
The experienced bricklayer takes 24 hours to do the job alone
check answer:
{{{(r + 2r)*12 = 3*(1/48)*12}}}
{{{(3/48)*12 = 3/4}}}
{{{r*12 = 12/48}}}
{{{12/48 = 1/4}}}
Working together, they did 3/4 of the job
Then the apprentice did 1/4 of the job alone