Question 427897
Working alone, two painters, A and B, can paint a building in 12 and 16 days respectively.
 After they work together for 3 days, A leaves and B continues for 2 more days.
 Then C joins B and they finish the job in 3 more days.
 In what time could C do the whole job alone?
:
Let c = time required by c to do the job alone
:
Let the completed job = 1
:
From the information we know that
A works for 3 days
B works 3 + 2 + 3 = 8 days
C works 3 days
:
{{{3/12}}} + {{{8/16}}} + {{{3/c}}} = 1
Reduce the fractions a common denominator of 4
{{{1/4}}} + {{{2/4}}} + {{{3/c}}} = 1
Multiply by 4c to clear the denominators, results:
c + 2c + 4(3) = 4c
:
3c + 12 = 4c
:
12 = 4c - 3c
:
c = 12 days alone is C's time
:
:
Check this:
{{{3/12}}} + {{{8/16}}} + {{{3/12}}} =
{{{1/4}}} + {{{2/4}}} + {{{1/4}}} = 1; confirms our solution of 12 days