A homeowner estimates that it will take him 12 days to roof his house. A professional roofer estimates that he could roof the house in 4 days. How long will it take if the homeowner helps the roofer?
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Let x = Number of days it will take the two to finish the job.
After x days, the homeowner has done x/12 of the job, while the roofer has done x/4 of the job. Furthermore,
( x / 4 ) + ( x / 12 ) = 1
multiply both sides by 36.
12x + 4x = 36
16x = 36
x = 36/16 = 2 1/4 days
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