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 km per hour and Birgit is walking in the opposite direction with a constant speed of 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 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 km per hour.
How many minutes after the departure of Anna and Birgit does mother return home?
Second Round, March, 2019
Solution
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