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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 ?
Found 2 solutions by JulietG, MathTherapy:
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.
Answer by MathTherapy(10803)  (Show Source):
You can put this solution on YOUR website!
A machine P can print one math book in 8 hours, machine Q can print the same number of
books (this author believes this should be PAGES) 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 ?
***************************************************************
The other person's answer, "approximately" 12:03 PM....", is WRONG!!
Machine P does the job (prints book) in 8 hrs, or does  of entire job in 1 hr
Machines P and Q do the job (print book) in 10 and 12 hrs, respectively
Then each does  and  of entire job in 1 hr, respectively
In 2 hours, the 3 machines complete  =  =  =  = 
Let the time it takes Q and R to complete the job, be T
Then working together, Q and R completes  of the job
We then get the following COMPLETE-JOB equation: T1(rates) + T2(rates) = 1 (entire job), OR
Fraction completed + Remaining Fraction = 1 (entire job). This produces:
37 + 6T + 5T = 60 ---- Multiplying by LCD, 60
37 + 11T = 60
11T = 60 - 37
11T = 23
Time it takes Q and R to complete the job, after P, Q, and R worked together for 2 hrs, or 
or 2 hrs, 5.5 minutes, approximately.
Finally, 2 hrs, 5.5 minutes after 11:00 a.m. takes us to 1:05.5, or approximately 1:06 p.m.
ANECDOTE
As seen above, the other person's approximated 1-hr claim is INVALID. The 3 machines completed of job in 2
hours, which leaves  of the job, incomplete. Does it make sense that 3 machines take 2 hours to complete ,
or >  of the job, but 2 of the 3 machines take just 1 hour to complete the remaining  (approximation),
especially when the FASTEST of the 3, P, is no longer working?
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