Question 1185232
Joe's rate,  {{{1/t}}}
Jay's rate, {{{1/(t+6)}}}
Their combined rate,  {{{1/4}}}


{{{1/t+1/(t+6)=1/4}}}
Simplify and solve.


{{{(t+6+t)/(t^2+6t)=1/4}}}

{{{(2t+6)/(t^2+6t)=1/4}}}

{{{4(2t+6)=t^2+6t}}}

{{{8t+24=t^2+6t}}}

{{{t^2-2t=24}}}

{{{highlight(t)(t-2)=24=6*4=highlight(6)(6-2)}}}


Joe needs 6 hours working alone and Jay needs 12 hours working alone.