SOLUTION: Tiburcio can paint a certain room in 1 day. His daughter Alma can paint it in 2 days. After Tiburcio has been working for several hours, his daughter helped him and together they f

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Tiburcio can paint a certain room in 1 day. His daughter Alma can paint it in 2 days. After Tiburcio has been working for several hours, his daughter helped him and together they f      Log On


   

Question 748787: Tiburcio can paint a certain room in 1 day. His daughter Alma can paint it in 2 days. After Tiburcio has been working for several hours, his daughter helped him and together they finished the job in 3 hours. How many hours did Tiburcio work alone? Assume an 8-hour working day.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Tiburcio can paint a certain room in 1 day.
His daughter Alma can paint it in 2 days.
After Tiburcio has been working for several hours, his daughter helped him and together they finished the job in 3 hours.
How many hours did Tiburcio work alone?
Assume an 8-hour working day.
:
Let t = time that Ti worked alone
Let the completed job = 1 (a painted room)
:
A shared work equation, (time in hrs)
%28%28t%2B3%29%29%2F8 + 3%2F16 = 1
multiply by 16, cancel the denominators, resulting in:
2(t+3) + 3 = 16
2t + 6 + 3 = 16
2t = 16 - 9
2t = 7
t = 7/2
t = 3.5 hrs worked by Ti alone
:
:
See if that checks out on a calc:
6.5%2F8 + 3%2F16 =
.8125 + .1875 = 1