SOLUTION: One person can do a job in 8 hours. A second person can do it in 12 hours. If the first person works 2 hours less than the second, how many hours will it take them working together

Question 171184: One person can do a job in 8 hours. A second person can do it in 12 hours. If the first person works 2 hours less than the second, how many hours will it take them working together?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let t=time it takes them working together
First person works at the rate of 1/8 job per hour
Second person works at the rate of 1/12 job per hour
Together they work at the rate of 1/8 + 1/12 =3/24 + 2/24 =5/24 job per hour
While the first person is not working for 2 hours, the second person will complete(1/12)*2=1/6 of the job, leaving 5/6 of the job yet to do. So, they both will work together to complete the remaining 5/6 of the job
So, our equation to solve is:
(5/24)*t=5/6 multiply each side by 24
5t=20
t=4 hours-------------time it takes them working together to finish the job.
CK
(1/12)*2+(5/24)*4=1 (1 job, that is)
1/6 +20/24=1
4/24 + 20/24=1
1=1
Hope this helps---ptaylor

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