And now for another typical discrepancy problem of mine. I would appreciate if you can help resolve this issue.
Brothers Barry, Carl, and Dave can each roof a house alone in 60 hours, 68 hours and 72 hours respectively. How long will it take the brothers to roof a house if Barry and Carl start together and Dave joins them for the second half of the job? (nearest hour).
My approach:
I first found the time it took for Barry and Carl to roof a house. There combined rate is $1$ house every $31.875$ hours. So it takes them $15.9375$ hours to complete the first "half of the job." When Dave enters the picture, their new effective rate is $277$ houses every $6120$ hours, or $\frac12$ every $11.047...$ hours. The combined time is, rounded to the nearest hour, is $27$ ($26.984$) hours, but the solution states that it is $26$ hours.
For those who think the difference is negligble (and it shouldn't be), it was a multiple choice question with the choices $27$ hours and $26$ hours. Can someone explain? Thank you.
I don't see anything wrong with your solution. There could be a problem with the solution key you're looking at.