WORD PROBLEM! IN SEARCH OF HELP! (intermediate algebra)

Question

A welder requires 24 h to do a job. After the welder and an apprentice work on the job for 12 h, the welder quits. The apprentice finishes the job in 13 h. How long would it take the apprentice, working alone, to do the job?

Answer 1

 

The Welder's rate is 1 job per 24 hours.  Expressed as a unit rate, the welder;s rate is

 

     1/24th job per hour

     = (1/24)/hr

 

 

Let x represent the apprentice's hourly rate.

 

Working together, the combined rate is (1/24) + x 

     

      rate • time = distance,  

      (1/24 + x)(12) =1/2 + 12x      

 

Working alone (the apprentice),

 

     rate • time = distance

     x •13 = 13x 

     

The combined scenarios results in a completed job, so we can add the 2 distance above.  The sum is 1 completed job

 

     1/2 + 12x + 13x = 1

     1/2 + 25x = 1

     1 + 50x = 2  ... multiply by 2 to clear the fraction

     50x = 2 - 1

     50x = 1

         x = 1/50

 

So the apprentice's rate is 1/50th of a job, per hour.

So it will take him 50 hours to do the job, if he is working alone.

 

 

         

Answer 2

welder's rate is 1/24 of the job in 1 hour

apprentice's rate is 1/x of the job in 1 hour

after 12 hours the welder quits

after 12 hours the welder did 1/2 of the job

the apprentice did (1/x)(12) of the job with the welder and (1/x)(13) of the job by himself which is 1/2 of the job done by the apprentice

(1/x)(12)+(1/x)(13)=1/2

(12/x)+(13/x)=1/2

multiply both sides by x

12+13=(1/2)(x)

25=(1/2)(x)

multiply both sides by 2

50=x

the apprentice takes 50 hours alone to do the job