SOLUTION: A can do a piece of work in 10 days. After he has worked 2 days, B came to help him and together they finished it in 3 days. In how many days could B alone have done the work? Plea

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A can do a piece of work in 10 days. After he has worked 2 days, B came to help him and together they finished it in 3 days. In how many days could B alone have done the work? Plea      Log On


   

Question 496656: A can do a piece of work in 10 days. After he has worked 2 days, B came to help him and together they finished it in 3 days. In how many days could B alone have done the work? Please give an answer. Thank you
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
In work problems, you add their rates of
working to get their rate working together.
A's rate is ( 1 job ) / ( 10 days ) = +1%2F10+
B's rate is ( 1 job ) / ( x days ) = +1%2Fx+
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The question to ask is: " What part of the job
does A get done in 2 days?"
If he does 1 job in 10 days, he does 1/10
of a job in 1 day. That means he does 2/10
or 1/5 of a job in 2 days.
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So, there is +1+-+1%2F5+=+4%2F5+ of the job left
to do when B joins him
So, they do 4/5 of the job together in 3 days
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Adding their rates of working:
+1%2F10+%2B+1%2Fx+=+%284%2F5%29%2F3+
+1%2F10+%2B+1%2Fx+=+4%2F15+
Multiply both sides by +30x+
+3x+%2B+30+=+8x+
+5x+=+30+
+x+=+6+
B alone could have done the work in 6 hours