The mushrooms picked by $2$ white rabbits in $3$ days will be eaten by $3$ gray rabbits in $4$ days. In how many days will $15$ gray rabbits eat up mushrooms picked by $5$ white rabbits in $6$ days? 
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The mushrooms picked by $2$ white rabbits in $3$ days will be eaten by $3$ gray rabbits in $4$ days, so the mushrooms picked by $1$ white rabbits in $1$ days will be eaten by $1$ gray rabbits in $2$ days.  Thus, the mushrooms picked by $5$ white rabbits in $6$ days will be eaten by $15$ gray rabbits in $4$ days. 