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

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

Start with the work done formula.

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

Plug in (for 1 job) and

Divide both sides by 20.

So the man's rate is of a wall per hour

Go back to the first formula

Plug in and

Divide both sides by x.

So the apprentice's rate is of a wall per hour

Now add the two rates to get

So together, their rate is

Go back to the first formula

Plug in , , and (this is the time for them if they work together)

Multiply both sides by .

Distribute

Subtract from both sides.

Combine like terms on the left side.

Divide both sides by to isolate .

Reduce.

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Answer:

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

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