SOLUTION: A worker can cover a parking lot with asphalt in ten hours. With the help of an assistant, they can do the job in six hours. How long would it take the assistant, working alone, to

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Question 92214: A worker can cover a parking lot with asphalt in ten hours. With the help of an assistant, they can do the job in six hours. How long would it take the assistant, working alone, to cover the parking lot with asphalt?
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Let's try to analyze the problem.
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Since the worker could do the job in ten hours, then each hour that goes by he does 1%2F10
of the job. So in 6 hours he does 6 times 1%2F10 which is 6%2F10 of the job.
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Meanwhile, we don't know how many hours it would take the assistant to do the job alone. So
let's call the T the amount of time it would take the assistant to do the job alone.
Therefore, in one hour the assistant would do 1%2FT of the job, and in 6 hours the assistant
would do 6 times 1%2FT or 6%2FT of the job.
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Next we can add the two 6-hour completions together and they would equal the 1 job. In
equation form this becomes:
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6%2F10+%2B+6%2FT+=+1
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Get rid of the 6%2F10 on the left side by subtracting 6%2F10 from both sides. This
subtraction results in the equation becoming:
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6%2FT+=+1+-+6%2F10+=+10%2F10+-+6%2F10+=+4%2F10
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(Note that the subtraction on the right side is just 1 - 0.6 = 0.4 or four tenths.)
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So we now have:
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6%2FT+=+4%2F10
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We can get rid of the denominators by multiplying both sides by 10T. This makes the equation
become:
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%2810T%2A+6%29%2FT+=+%2810T%2A4%29%2F10
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Cancel the like terms in the numerators with their corresponding terms in the denominators:
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%2810%2Across%28T%29%2A6%29%2Fcross%28T%29+=+%28cross%2810%29%2AT%2A4%29%2Fcross%2810%29
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and the equation that remains is:
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10%2A6+=+4%2AT
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Multiply the left side and the equation becomes:
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60+=+4%2AT
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And finally, solve for T by dividing both sides by 4 to get:
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60%2F4+=+T
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and this simplifies to:
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15+=+T
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This tells us that the assistant could finish the job alone in 15 hours.
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Check ... In 6 hours the worker completes six tenths of the job (one tenth each hour) and
in the same 6 hours the assistant would complete 1%2F15 of the job each hour or
6%2F15 during the 6 hours. Note that 6%2F15 divides out to be 0.4 which is the
four tenths of the work that the worker would not finish. So the six tenths of the job
plus the four tenths of the job means that the job is complete in six hours when they work
as a team. Our 15 hours for the assistant to do the job alone is correct.
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Hope this analysis approach helps you to understand the problem a little better.
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