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Three sisters decide to paint a wall. The eldest sister could have painted it herself in 3 hours, the middle sister would have taken 4 hours and the youngest would have taken 6. How long will it take them to paint the wall working together?
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In an hour the eldest sister can paint a third of the wall, the middle sister can paint a quarter of the wall and the youngest sister can paint a sixth of the wall. So together they can paint
$$\frac{1}{3}+\frac{1}{4}+\frac{1}{6}=\frac{4+3+2}{12}=\frac{9}{12}=\frac{3}{4}$$
by Diamond (75,934 points)
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