SOLUTION: Two painters, working together, can paint a house in 3 days. One painter working alone can paint the house in 4 days. How many days would it take the second painter, working alon

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Question 994052: Two painters, working together, can paint a house in 3 days.
One painter working alone can paint the house in 4 days.
How many days would it take the second painter, working alone,to paint the house.
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52879) About Me  (Show Source):
You can put this solution on YOUR website!
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Two painters, working together, can paint a house in 3 days.
One painter working alone can paint the house in 4 days.
How many days would it take the second painter, working alone,to paint the house.
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Let  x  be the number of days for the second painter to paint the house,  working alone.
Then the second painter paints  1%2Fx  of the house per day.  It is his rate of work.

The first painter can paint  1%2F4  of the house per day.  It is his rate of work.

Working together, they paint 1%2F3 of the house per day.

It gives an equation

1%2F4 + 1%2Fx = 1%2F3.

Simplify and solve it.  Multiply both sides by  12x  (it is the common denominator).  You will get

3x + 12 = 4x.

Hence, x = 12.

Answer.  The second painter can paint the house in  15  days.

For more problems on joint work see the lesson  Using fractions to solve word problems on joint work  in this site.


Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!

Two painters, working together, can paint a house in 3 days.
One painter working alone can paint the house in 4 days.
How many days would it take the second painter, working alone,to paint the house.
Time 2nd painter takes, alone: highlight_green%2812%29 days