When both printers Y and Z are used, a collection of books can be printed in 3 hours. While printing, Printer Y broke down. As a result, it took 8 hours to complete printing. If it would take Printer Z 12 hours to print the collection alone,
- How long would it take to print the collection of books using only Printer Y? Express your answer in hours.
- How long was Printer Y used before it broke down? Express your answer in hours.
(a)
Time taken by Printer Y and Z:
3 h → 1 collection of books
1 h → 1 ÷ 3 =
13 collection of books
Time taken by only Printer Z:
12 h → 1 collection of books
1 h → 1 ÷ 12 =
112 collection of books
Time taken by only Printer Y:
1 h →
13 -
112 =
14 collection of books
1 collection of books → 1 ÷
14 = 1 x 4 = 4 h
(b)
Time taken by only Printer Z:
8 h → 8 x
112 =
23 collection of books
Fraction of the collection of books to be done by Printer Y
= 1 -
23=
13 Time taken by Printer Y before it broke down:
13 collection of books →
13 ÷
13 =
13 x
31 = 1 h
Answer(s): (a) 4 h; (b) 1 h