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It takes $30$ minutes to empty a half-full tank by draining it at a constant rate. It is decided to simultaneously pump water into the half-full tank while draining it. What is the rate at which water has to be pumped in so that it gets fully filled in $10$ minutes?

- $4$ times the draining rate
- $3$ times the draining rate
- $2.5$ times the draining rate
- $2$ times the draining rate