Question 850681
<pre>
A machine P can print one math book in 8 hours, machine Q can print the same number of <font color = red><b><s>
books</s> (this author believes this should be PAGES)</font></b> 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 ?
***************************************************************<font color = blue><font  size = 2><font face  -  tahoma><b>
The other person's answer, "approximately" 12:03 PM....", is WRONG!!

Machine P does the job (prints book) in 8 hrs, or does {{{(1/8)^(th)}}} of entire job in 1 hr

Machines P and Q do the job (print book) in 10 and 12 hrs, respectively
Then each does {{{(1/10)^(th)}}} and {{{(1/12)^(th)}}} of entire job in 1 hr, respectively

In 2 hours, the 3 machines complete {{{2(1/8 + 1/10 + 1/12)}}} = {{{2/8 + 2/10 + 2/12}}} = {{{1/4 + 1/5 + 1/6}}} = {{{(15 + 12 + 10)/60}}} = {{{37/60}}}

Let the time it takes Q and R to complete the job, be T
Then working together, Q and R completes {{{T(1/10 + 1/12)}}} 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: 
                                                        {{{37/60 + T(1/10 + 1/12) = 1}}}
                                                           {{{37/60 + T/10 + T/12 = 1}}}
                                                          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 {{{matrix(1,2, T = 23/11 = 2&1/11, hrs)}}}
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.


<u>ANECDOTE</u>
As seen above, the other person's approximated 1-hr claim is INVALID. The 3 machines completed {{{37/60}}} of job in 2
hours, which leaves {{{23/60}}} of the job, incomplete. Does it make sense that 3 machines take 2 hours to complete {{{37/60}}},
or > {{{1/2}}} of the job, but 2 of the 3 machines take just 1 hour to complete the remaining {{{1/3}}} (approximation),
especially when the FASTEST of the 3, P, is no longer working?</font></font></font></b></pre>