# Three painters

One painter would have painted the fence for 15 hours, the second in 12 hours. The plot had to be painted in four hours, so they called the third one, and all worked together. For what time would the third painter paint fence the fence alone?

Result

x =  10 h

#### Solution:

$4 \cdot \ (1/15+1/12+1/x)=1 \ \\ \ \\ \ \\ 4 \cdot \ (x/15+x/12+1)=x \ \\ \ \\ 24x=240 \ \\ \ \\ x=10 \ \\ =10 \ \text{h}$

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