Question 821516
Jonjon's rate: 1/8 jobs per hour
Brother's rate: 1/20 jobs per hour


Jonjon works for h hours and his brother works for h/2 hours and the amount of the job, 1, will be done.
{{{highlight_green((1/8)h+(1/20)(h/2)=1)}}}
{{{h(1/8+1/40)=1}}}
{{{h(5/40+1/40)=1}}}
{{{h(6/40)=1}}}
{{{h(3/20)=1}}}
{{{h=(20/3)*1=highlight(2&6/7)}}} hours, maybe not what you really wanted.


They work TOGETHER?
{{{highlight(highlight(((1/8)+(1/20))(h/2)+(1/8)h=1))}}}, for some part of the work they work at their combined rate and for the rest of the work, only Jonjon works.  This equation may better be what you want.
'
{{{(1/16+1/40)h+(1/8)h=1}}}
{{{4*40(1/16+1/40)h+40(1/8)h=4*40}}}
{{{(10+4)h+5h=160}}}
{{{14h+5h=160}}}
{{{19h=160}}}
{{{h=160/19}}}
{{{highlight(h=8&8/19)}}} hours for Jonjon alone,
{{{highlight(h/2=80/19=4&4/19)}}} hours Jonjon and his brother together.