SOLUTION: A painter can paint a building in 15 days and a co worker can do the same job in 10 days. If the first painter starts and 3 days later the co worker Joins in to help finish the job

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Question 1115560: A painter can paint a building in 15 days and a co worker can do the same job in 10 days. If the first painter starts and 3 days later the co worker Joins in to help finish the job, how many does it take to paint the building?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39618) About Me  (Show Source):
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Rate of a painter, 1%2F15.
Rate of co-worker, 1%2F10.

Painting the building is 1 job.

%281%2F15%29%2A3%2B%281%2F15%2B1%2F10%29%2Ax=1
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1%2F5%2B%282%2F30%2B3%2F30%29x=1
1%2F5%2B%285%2F30%29x=1
1%2F5%2B%281%2F6%29x=1, LCD is 30.

30%281%2F5%2Bx%2F6%29=30
6%2B5x=30
5x=24
x=24%2F5


If counting nearest whole days then 5 days; total of 8 days.
If counting fractions of any day, then 4%264%2F5; total of 7%264%2F5.

Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.
1.  From the condition, the first painter makes  1%2F15  of the job per day.

    The second makes 1%2F10  of the job per day.


    Hence, working together, they make  1%2F15+%2B+1%2F10 = 2%2F30+%2B+3%2F30 = 5%2F30 = 1%2F6  of the job per day.

    It is their combined rate of work.



2.  Working for 3 days, the first painter made  3%2F15 = 1%2F5 of the job.

    Hence,  4%2F5 of the job remained.



3.  Thus the two, working together, must complete  4%2F5 of the job.

    Since their combined rate of work is  1%2F5 of the whole work per day,
    it will take them   %28%284%2F5%29%29%2F%28%281%2F6%29%29 = %286%2A4%29%2F5 = 24%2F5 of the day = 44%2F5 days = 4.8 days.

Answer.  The schedule is this:  first painter works 3 days,  and then the two work together for  4.8 days.


Solved.