How long for each to do job?

Question

An experienced worker can do a job twice as fast as an apprentic. If they work together, they can do a job in 3 hours. How long would it take each to work individuallay?

Answer 1

The experienced worker works at twice the speed of the apprentice so let's call his part of any given job 2x and call the Apprentice's part of the job x.

 

When the work together they are ADDING there efforts so, if a job takes 3 hours than, it can be expressed as:

 

        2x       +     x     =  one whole job, 

      Master      Apprentice

Then:

          3x =  1 job.

and       x  =   1/3 of the the job.

 

So the apprentice would to 1/3 of any job, and the master would do 2/3 of any job.

 

A job that took 3 hours for them to do together would take 3 times as long for the apprentice on his own.

 

So, 9 hours for the apprentice.

 

A same job would be 2/3 done by the master alone in the 3 hours. The amount of work remaining is 1/2, of what he was able to do in 3 hours, so, 3 hours plus 1/2 of three hours (1.5)  is 4 1/2 hours total.

 

It would take the master 4 1/2 hours to do the job alone.

 

Notice, that this double checks with the stated work rates.  The apprentice took twice as long (9 hours) as the master (4 1/2 hours) to do the job solo.