<PRE><B>Question 276491</B>
If 5 adults and 2 children work together, a job can be done in a day. 
If only 2 adults work, then 6 children must work in order to complete the job in a day.
 The number of days that it takes for a child to do the job alone is: 
:
Let a = time required when adult does the job alone
let c = time required when a child does it
:
Let the completed job = 1
:
{{{5/a}}} + {{{2/c}}} = 1
and
{{{2/a}}} + {{{6/c}}} = 1
:
Therefore:
{{{2/a}}} + {{{6/c}}} = {{{5/a}}} + {{{2/c}}}
{{{6/c}}} - {{{2/c}}} = {{{5/a}}} - {{{2/a}}}
{{{4/c}}} = {{{3/a}}} 
Cross multiply
4a = 3c
a = {{{3/4}}}c
a = .75c
:
Using the 1st equation replace a with .75c, find c
{{{5/(.75c)}}} + {{{2/c}}} = 1
Multiply equation by 3c, results
4(5) + 3(2) = 3c
20 + 6 = 3c
c = {{{26/3}}} days for a child alone

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