SOLUTION: A librarian arranges books in 3 hours. A volunteer student can do the same job in 5 hours. If they work together for 1 hour and the student leaves then how much longer does the lib

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A librarian arranges books in 3 hours. A volunteer student can do the same job in 5 hours. If they work together for 1 hour and the student leaves then how much longer does the lib      Log On


   

Question 768510: A librarian arranges books in 3 hours. A volunteer student can do the same job in 5 hours. If they work together for 1 hour and the student leaves then how much longer does the librarian have to work?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The task of arranging the books takes 3 hours of work by the librarian.
That means that the libraraian completes 1%2F3 of the job in 1 hour.
That is the librarians speed/rate of work.
The volunteer student is slower.
He/she needs 5 hours to do the same work, and that means that his/her speed/rate of work is
1%2F5 of the task pe hour.
Working together for 1 hour, they complete
1%2F3%2B1%2F5=5%2F15%2B3%2F15=8%2F15 of the work of arranging the books.
That means that the fraction of the job remaining is 1-8%2F15=7%2F15 of the job.
That much work is left for the librarian to finish alone.
At a rate of 1job%2F%223+hours%22=1%2F3 of the job per hour, it will take the librarian
%28%22%287%2F15%29job%22%29%2F%28%281job%2F%223+hours%22%29%29=%287%2F15%29job%283hours%2F%221+job%22%29=7%2F5hour.
Calculating it as hours and minutes:
7%2F5hour=1%262%2F5hour and 2%2F5hour%2860minutes%2F%221+hour%22%29=24minutes
The librarian will have to work 1 hour and 24 minutes longer after the volunteer student leaves.