Question 1181303
<pre>
Carlo can type a manuscript for 10 hours. he started working then bobby joined him 2 hours later. they worked together for 4 hrs
until carlo decided to stop and then bobby had to finish the manuscript alone. if bobby finished the remaining portion in 6 more
hours, how long can he type the whole manuscript working alone?

Carlo can complete the job in 10 hours, or {{{1/10}}} of job in 1 hr
Let time Bobby takes, to do entire job, by himself, be B
Then, Bobby can complete {{{1/B}}} of job in 1 hr

Since Bobby started 2 hours after Carlo, then Carlo worked alone for 2 hours. So, fraction of job completed by Carlo,
before Bobby joined him = {{{2(1/10) = 2/10}}}
With both working together for 4 hrs, fraction of job both completed, working together = {{{4(1/10 + 1/B)}}}
Finally, given that Bobby completed the remaining portion in 6 hours, fraction of entire job done by Bobby, alone, = {{{6(1/B)}}}. 
We then get the following ENTIRE JOB-equation: {{{2/10 + 4(1/10 + 1/B) + 6(1/B) = 1}}}
                                                       {{{2/10 + 4/10 + 4/B + 6/B = 1}}}
                                                            {{{6/10 + 10/B = 1}}}
                                                          6B + 100 = 10B ----- Multiplying by LCD, 10B
                                                               100 = 10B - 6B
                                                               100 = 4B
<font color = red><font size = 4><b>Time taken by Bobby to do the ENTIRE job, working ALONE</font></font></b>, or {{{matrix(1,5, B, "=", 100/4, "=", highlight(matrix(1,2, 25, hours)))}}}</pre>