Question 424737
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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.<br>
But you can get good mental exercise (and good problem-solving experience!) by solving the problem informally, using logical reasoning and simple arithmetic.<br>
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.<br>
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.<br>
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.<br>
2/3 of 8 hours is 16/3 hours, or 5 1/3 hours.<br>
ANSWER: 5 1/3 hours<br>