Suppose a group of three athletes must race a distance d. The athletes have two bikes, each of which can accomodate only one rider at a time. All three athletes are equally fast and each can run the distance d in time r, or bike the distance d in time b, where b < d. What is the optimal solution for reaching the goal the fastest? |

At first look, it seems like the team can only move as fast as the runner, which would mean that the team could finish in time r. But as it turns out, an optimal solution can cut this down to r/3 + 2*b/3.Let's call our athletes Denis, Don, and Rob. At the start, Denis starts running while Don and Rob start biking as fast as they can. Don stops at a distance d/3 and starts running, leaving his bike for the Denis while Rob continues to bike ahead. Rob stops at a distance 2*d/3 and starts running to the finish, leaving his bike for Don. Even though the racers are separated for most of the race, they should arrive at the finish line simultaneously, each having run one third and biked two thirds of the race. |

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