Vavilen inflated a huge balloon in $19$ minutes. Then he poked a hole in the balloon so that it slowly leaked air out until it was completely deflated. The rate at which the air leaked out of the balloon (in liters of air per minute) was half of the rate at which Vavilen inflated the balloon. It took the balloon $38$ minutes to completely deflate. **At what rate did Vavilen inflate the balloon, and at what rate did the balloon deflate?** [[☃ radio 1]]