SOLUTION: A homeowner estimates that it will take her 7 days to roof her house. A professional roofer estimates that he could roof the house in 2 days. How long will it take if the home owne

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A homeowner estimates that it will take her 7 days to roof her house. A professional roofer estimates that he could roof the house in 2 days. How long will it take if the home owne      Log On


   

Question 818894: A homeowner estimates that it will take her 7 days to roof her house. A professional roofer estimates that he could roof the house in 2 days. How long will it take if the home owner helps the roofer?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Each of them might work according to his stated, given work speed. The work speeds are additive.

Use the speeds (rates) in the form of roofs per day.
Homeowner rate plus roofer rate equals their combined rate:
%281%2F7%29%2B%281%2F2%29=2%2F14%2B7%2F14=highlight%289%2F14%29 roofs per day, like 9 roofs in 14 days.

You are interested in the reciprocal, 14%2F9=highlight%281%265%2F9%29 day for 1 roof.
A more realistic interpretation requires a little more information about how many hours per day is given for any day's work.