SOLUTION: I can't figure out the . I need help, please! It takes Pat 12 hours to complete a task. After he had been working for 3 hours, his brother Mike joined him, and together they finis

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Question 4603: I can't figure out the . I need help, please!
It takes Pat 12 hours to complete a task. After he had been working for 3 hours, his brother Mike joined him, and together they finished the job in 5 hours. How long would it take Mike to do the job by himself?
Answer by Abbey(339) About Me  (Show Source):
You can put this solution on YOUR website!
To find a rate of work, break the problem down into something that can be compared relatively easily. In this case, look at how much work Pat gets done each hour.
Pat = completes 1%2F12 of the work every hour
Mike's rate of work is not known so we can say
Mike= completes 1%2Fx of the work every hour.
Together they work at a rate of 1/5 of the work completed each hour, so:
1%2F12+%2B+1%2Fx+=+1%2F5
Find a common denominator:
5x%2F60x%2B60%2F60x=12x%2F60x
Now we can drop the denominator:
5x+60=12x
subtract 5x from both sides:
60=7x
divide both sides by 7:
60/7=x or x=8.57
so Mike's rate of work is 1%2F8.57, so he could finish the job in 8.57 hours by himself.