SOLUTION: A welder can complete a job in 20 hours. The welder and her apprentice work together on the job for 10 hours. Then the welder leaves for another project and her apprentice finishes

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A welder can complete a job in 20 hours. The welder and her apprentice work together on the job for 10 hours. Then the welder leaves for another project and her apprentice finishes      Log On


   

Question 870493: A welder can complete a job in 20 hours. The welder and her apprentice work together on the job for 10 hours. Then the welder leaves for another project and her apprentice finishes the job in five hours. How long would it take the apprentice to do the entire job working alone? Let x = the time for the apprentice to complete the job working alone
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The welder's rate of working is:
( 1 job ) / ( 20 hrs )
The apprentice's rate of working is:
( 1 job ) / ( x hrs )
-----------------------------
Add their rates of working to
find out what fraction of the job they
get done working together for +10+ hrs
let +y+ = the fraction
---------------------------
+1%2F20+%2B+1%2Fx+=+y%2F10+
+y+=+10%2A%28+1%2F20+%2B+1%2Fx+%29+
+y+=+1%2F2+%2B+10%2Fx+
------------------------------
The fraction of the job remaining to be
done is:
+1+-+1%2F2+-+10%2Fx++=+1%2F2+-+10%2Fx+
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Since the apprentice's rate is +1%2Fx+,
+1%2Fx+=+%28%28+1%2F2+-+10%2Fx+%29%29+%2F+5+
Multiply both sides by +5x+
+5+=+x%2A%28+1%2F2+-+10%2Fx+%29+
+5+=+x%2F2+-+10+
+x%2F2+=+15+
+x+=+30+
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The apprentice can do the entire job
working alone in 30 hrs