SOLUTION: 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 e

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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): You can put this solution on YOUR website!
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?
:
let p = time required by Pat doing the job alone
let the completed job = 1
:
From the given information we know: L worked 5 hrs and P worked 2 hrs
:
+ = 1
multiply by 8p to clear the denominators, results:
5p + 8(2) = 8p
16 = 8p - 5p
16 = 3p
p =
p = 5 hrs alone
:
:
Check this using decimals
5/8 + 2/5.33
.625 + .375 = 1.0

Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
Larry:
workrate,

Patrick:
workrate,

Larry painted for 3 hour and then both worked 2 hours together to finish 1 job.







Answer by ikleyn(52813)   (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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