<PRE><B>Question 126412</B>
Ron Wood can paint a room in 6 hr working alone. If his son, Jason, helps him, the job takes 4 hr. How long would it take Jason to do the job if he worked alone?
:
A typical shared work equation:
:
Let t = time required if J works alone
:
Let the completed job = 1; (each will do a fraction of the job)
:
{{{4/6}}} + {{{4/t}}} = 1
:
Multiply equation by 6t to get rid of the denominators:
6t*{{{4/6}}} + 6t*{{{4/t}}} = 6t(1)
Cancel out the denominators, resulting in
:
4t + 6(4) = 6t
:
4t + 24 = 6t
:
24 = 6t - 4t
:
24 = 2t
:
t = 12 hrs, J working alone 
:
Check solution:
{{{4/6}}} + {{{4/12}}} = 
{{{2/3}}} + {{{1/3}}} = 1</PRE>