Second Round, March 2019

After breakfast, the sisters Anna and Birgit depart for school, each going to a different school. Their house is next to a bicycle path running between the two schools. Anna is cycling with a constant speed of $12$ km per hour and Birgit is walking in the opposite direction with a constant speed of $4$ km per hour. They depart at the same time. Shortly after their departure, mother notes that the girls have forgotten their lunch and decides to go after them. Exactly $10$ minutes after Anna and Birgit have left, mother departs on her electric bike. First, she catches up with Anna. She hands her a lunch box, immediately turns around, and goes after Birgit. When she catches up with Birgit, she hands her a lunch box and immediately rides back home. Mother always rides at a constant speed of $24$ km per hour. How many minutes after the departure of Anna and Birgit does mother return home?