how long does it take each to do the job alone??

Question

A homeowner estimates that it will take him 5 days more than a professional roofer to repair the roof of his house. together they can do the job in 6 days.

Answer 1

1/(5+p) + 1/p = 1/6

multiply by 6(p)(5+p)

6p + 6(5+p) = p(5+p)

6p + 6p + 30 = 5p + p^2

p^2 -7p - 30 = 0

(p-10)(p+3) = 0

p=10 hours for the pro alone

15 hours for the homeowner alone

1/15 + 1/10 = 1/6

2/30 + 3/30 = 5/30 = 1/6

If they worked at the same rate they'd do it each alone in 6x 2 = 12 hours

12 is roughly the average of 15 and 10