Question 182495
Let x=no. of days it will take the two to finish the job.
...
After x days, the homeowner has done x/9 of the job, while the roofer has done x/4 of the job. Furthermore,

(x/4)+(x/9)=1
multiply both sides by 36.
9x+4x=36
13x=36
x=36/13=2 10/13 days

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