SOLUTION: A man can construct a wall in 20 hrs. With the help of his apprentice assistant the task would take 12 hrs. How long would it take the apprentice, working alone, to construct the

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A man can construct a wall in 20 hrs. With the help of his apprentice assistant the task would take 12 hrs. How long would it take the apprentice, working alone, to construct the      Log On


   

Question 152882: A man can construct a wall in 20 hrs. With the help of his apprentice assistant the task would take 12 hrs. How long would it take the apprentice, working alone, to construct the wall?

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=# of hours apprentice can complete the job


W=RT Start with the work done formula.

Since the "man can construct a wall in 20 hrs", this means that T=20


1=R%2820%29 Plug in W=1 (for 1 job) and T=20


1%2F20=R Divide both sides by 20.


So the man's rate is 1%2F20 of a wall per hour


W=RT Go back to the first formula


1=Rx Plug in W=1 and T=x


1%2Fx=R Divide both sides by x.


So the apprentice's rate is 1%2Fx of a wall per hour


Now add the two rates to get R=1%2F20%2B1%2Fx=x%2F%2820x%29%2B20%2F%2820x%29=%28x%2B20%29%2F%2820x%29


So together, their rate is R=%28x%2B20%29%2F%2820x%29


W=RT Go back to the first formula


1=%28%28x%2B20%29%2F%2820x%29%29%2812%29 Plug in W=1, R=%28x%2B20%29%2F%2820x%29, and T=12 (this is the time for them if they work together)


20x=12%28x%2B20%29 Multiply both sides by 20x.


20x=12x%2B240 Distribute


20x-12x=240 Subtract 12x from both sides.


8x=240 Combine like terms on the left side.


x=%28240%29%2F%288%29 Divide both sides by 8 to isolate x.


x=30 Reduce.


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Answer:

So the answer is x=30 which means that it'll take 30 hours for the apprentice to do it alone.