SOLUTION: Jonjon can do a job in 8 hrs. His brother Paul can do the same job in 20 hrs. the brothers will do the job together with Paul working and a half times as long as Jonjon. How long w

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Question 821516: Jonjon can do a job in 8 hrs. His brother Paul can do the same job in 20 hrs. the brothers will do the job together with Paul working and a half times as long as Jonjon. How long will each brother work to complete the job together?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
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%28%281%2F8%29h%2B%281%2F20%29%28h%2F2%29=1%29
h%281%2F8%2B1%2F40%29=1
h%285%2F40%2B1%2F40%29=1
h%286%2F40%29=1
h%283%2F20%29=1
h=%2820%2F3%29%2A1=highlight%282%266%2F7%29 hours, maybe not what you really wanted.

They work TOGETHER?
highlight%28highlight%28%28%281%2F8%29%2B%281%2F20%29%29%28h%2F2%29%2B%281%2F8%29h=1%29%29, 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.
'
%281%2F16%2B1%2F40%29h%2B%281%2F8%29h=1
4%2A40%281%2F16%2B1%2F40%29h%2B40%281%2F8%29h=4%2A40
%2810%2B4%29h%2B5h=160
14h%2B5h=160
19h=160
h=160%2F19
highlight%28h=8%268%2F19%29 hours for Jonjon alone,
highlight%28h%2F2=80%2F19=4%264%2F19%29 hours Jonjon and his brother together.