Question 424737: larry can paint the walls of his apartment in 8h. after he has worked for 3h, patrick joins him , and together they finish the job in 2h. how long would it take patrick to do the entire painting job without larry?
Found 4 solutions by ankor@dixie-net.com, josgarithmetic, ikleyn, greenestamps:
Answer by ankor@dixie-net.com(22740)   (Show Source):
Answer by josgarithmetic(39620)  (Show Source):
Answer by ikleyn(52810)  (Show Source):
You can put this solution on YOUR website! .
Wow !
According to the ID number, this problem is about 15 years old (or about it !).
And was solved by another tutor, ankor@dixie-net.com, about 15 years ago ! !
Answer by greenestamps(13203)  (Show Source):
You can put this solution on YOUR website!
A formal algebraic solution like the one shown in the response from the other tutor is fine; and probably a formal algebraic solution was wanted.
But you can get good mental exercise (and good problem-solving experience!) by solving the problem informally, using logical reasoning and simple arithmetic.
Larry takes 8 hours to do the job himself, and he worked for 3 hours before Patrick joined him. So 3/8 of the job is done; 5/8 of it remains to be done.
In the next 2 hours that it takes the two of them to finish the job, Larry does another 2/8 of the job, which means Patrick does 3/8 of the job.
Since Patrick does 3/8 of the job in the time Larry does 2/8, Patrick's rate of work is 3/2 Larry's rate; that means he can complete the whole job alone in 2/3 the time it takes Larry to do the job alone.
2/3 of 8 hours is 16/3 hours, or 5 1/3 hours.
ANSWER: 5 1/3 hours
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