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Two pipes can fill a tank in 15 hours and 4 hours, respectively, while a third pipe can empty it in 12 hours. How long (in hours) will it take to fill the empty tank if all the three pipes are opened simultaneously?
$$ \frac{50}{7}$$
$$\frac{15}{7}$$
$$\frac{30}{7}$$
$$\frac{20}{7}$$
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