Question 82986
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A mechanic requires 2 h to repair a tranmission, whereas an apprentice
requires 6 h to make the same repairs. the mechanic worked alone for
1 h and then stopped. how long will it take the apprentice. working 
alone. to complete the repair? 

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This is a DRT problem, where "D" doesn't stand for "Distance", but
stands for "DEEDS DONE", or "fraction of a deed done". So make the 
following chart.  There are four situations to consider:

                                   Deeds     Rate       Time
Mechanic doing 1 complete job                                 
Apprentice doing 1 complete job                              
Mechanic doing partial job                                   
Apprentice doing partial job

Let the answer to the question:  

>>...How long will it take the apprentice. working alone. to complete the repair?...<< 
   
be t.  So fill in t for the time for the apprectice to do the partial
job of completing the job after the mechanic stops.

                                   Deeds     Rate       Time
Mechanic doing 1 complete job                                
Apprentice doing 1 complete job                             
Mechanic doing partial job                                   
Apprentice doing partial job                              t

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>>..A mechanic requires 2 h to repair a tranmission..<<

That's 1 deed in 2 hours, so fill in 1 deed and 2 hours on
the top row:

                                   Deeds     Rate       Time
Mechanic doing 1 complete job        1                    2
Apprentice doing 1 complete job                             
Mechanic doing partial job                                   
Apprentice doing partial job                              t

-------------------------------------

>>..an apprentice requires 6 h to make the same repairs..<<

That's 1 deed in 6 hours, so fill in 1 deed and 2 hours on
the second row:

                                   Deeds     Rate       Time
Mechanic doing 1 complete job        1                    2
Apprentice doing 1 complete job      1                    6 
Mechanic doing partial job                                    
Apprentice doing partial job                              t

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Next we use the formula R = {{{D/T}}} to fill in the rates
on the two top lines:

                                   Deeds     Rate       Time
Mechanic doing 1 complete job        1        1/2         2
Apprentice doing 1 complete job      1        1/6         6 
Mechanic doing partial job                                 
Apprentice doing partial job                              t

--------------------------------------

Now, since the mchanic and the apprentice doing the partial
jobs work at the same rates as when they do 1 complete job,
we can fill in {{{1/2}}} and {{{1/6}}} for the rates in the bottom two
rows:

                                   Deeds     Rate       Time
Mechanic doing 1 complete job        1        1/2         2
Apprentice doing 1 complete job      1        1/6         6 
Mechanic doing partial job                    1/2         1
Apprentice doing partial job                  1/6         t

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Next we use the formula D = RT to finish filling in the chart:

                                   Deeds     Rate       Time
Mechanic doing 1 complete job        1        1/2         2
Apprentice doing 1 complete job      1        1/6         6 
Mechanic doing partial job          1/2       1/2         1
Apprentice doing partial job        t/6       1/6         t

Now that the chart is complete, we form the equation by observing

the partial job which the mechanic did + the partial job which the apprentice
did = 1 complete job:

        
                            1/2 + t/6 = 1

Can you solve that?  If not post again asking how.

                        Answer: t = 3 hours.


Actually you can check it easy because you can do the whole 
thing in your head by looking at it this way. The mechanic 
does a whole job in 2 hours.  So in the one hour he worked, 
he did half the job. That leave the other half of the job to 
be done by the apprentice.  The apprentice can do a whole job 
in 6 hours, so he can do the remaining half-job which the 
mechanic left him with in half that time, or 3 hours.

Edwin</pre>