SOLUTION: A machine P can print one math book in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at

Question 850681: A machine P can print one math book in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 A.M. while machine P is closed at 11 A.M. and the remaining two machines complete work. Approximately at what time will the work (to print one math book) be finished ?
Answer by JulietG(1812) (Show Source): You can put this solution on YOUR website!
We're assuming that the book can be made up of pieces.
P * 8 = 1
Q * 10 = 1
R * 12 = 1
.
or the inverse:
P = 1/8
Q = 1/10
R = 1/12
.
P prints 1/8 * 2 hours; 2/8 of a book.
In the same time, Q prints 2/10
In the same time, R prints 2/12
.
After 2 hours, 2/8 + 2/10 + 2/12 of a book is printed. (1/4 + 1/5 + 1/6)
Let's use a common denominator for 4,5,6 --> 60
After 2 hours, 15/60 + 12/60 + 10/60 is finished, or 37/60.
.
Each following hour,
Q prints 2/10 (or 12/60)
R prints 2/12 (or 10/60)
.
After 3 hours, 37/60 + 22/60 is finished. That is 59/60.
.
Since Q and R print 22/60 per hour (or at the rate of 2.728 minutes), the remaining 1/60 is printed at 12:02.728, or "approximately" 12:03 PM.
.
*sigh* This sounds like one of those horrible Common Core messes.
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