59. Petya and Vasya calculated that if they walk to the neighboring village, which is four kilometers away from them, at a speed of 4 km per hour, they will be 10 minutes late for the football match being held there for the district championship. How should they act to arrive at the match simultaneously and gain the maximum time advantage, given that they have a bicycle at their disposal, on which only one person can ride, but three times faster than walking? How many minutes before the start of the match will they arrive in this case?
59. To arrive simultaneously and gain the most time, Petya and Vasya should do the following: one of them rides the bicycle, while the other walks. After covering half the distance, the first one leaves the bicycle and continues on foot. The second one, upon reaching the bicycle, picks it up and rides it to the end of the journey. In this way, each of them walks half the distance and rides the other half, so they arrive at the destination simultaneously. (Under other conditions, they cannot arrive simultaneously.) If Petya and Vasya walk the entire distance, they will spend 1 hour. But since this would make them 10 minutes late, the match starts 50 minutes after they leave ( $60-10=50$ ). If, however, they walk half the distance and ride the bicycle for the other half, it will take them 40 minutes ( $60: 2+(60: 2): 3=30+10=40$ ). This means the boys will arrive 10 minutes before the match starts ( $50-40=10$ ).

Note. The bicycle can be left at any equal segments of the journey.

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