Question

Mrs. hensen cataloged a group of incoming library books in 8 hours. mr. taylor can catalog the same number of books in 4 hours. mrs. phillips can catalog them in 6 hours. how long would it take if they all worked together?

Answer 1

Let n = the number of books.

Mrs. Hensen's working rate is
x = n/8 books/h
Mr. Taylor's working rate is
y = n/4 books/h
Mrs. Phillip's working rate is
z = n/6 books/h

When they work together, they can catalog n books in
(n books)/(x+y+z books/h)
= n/(n/8 +n/4 + n/6)
= 1/(1/8 + 1/4 + 1/6)
= 1/(13/24)
= 24/13 hours

The time required is 24/13 h = 1.8462 h = 1 hour, 51 min

Answer: 1.8462 hours (or 1 hour, 51 minutes)