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The first thing you should know is that the distance is equal to the speed per time.
Therefore if You walk forward at 1.5 m / s for 8s
d = 1.5t [0,8] s
Your friend decides to walk faster and starts at 2.0 m / s for the first 4 s.
d = 2t [0,4] s
Then she slows down and walks forward at 1.0 m / s for the next 4s
d = t + 4 [4,8] s
Who walked farther?
They both walked the same distance
12 meters
Therefore if You walk forward at 1.5 m / s for 8s
d = 1.5t [0,8] s
Your friend decides to walk faster and starts at 2.0 m / s for the first 4 s.
d = 2t [0,4] s
Then she slows down and walks forward at 1.0 m / s for the next 4s
d = t + 4 [4,8] s
Who walked farther?
They both walked the same distance
12 meters
There are two interchangeable concepts that can be applied to this theory. The first one is the moment of Inertia and the second the perioricity. When the runners put their leg forward they reduce their moment of inertia allowing their center of mass to maintain the speed they carry and not waste energy. In this way when they swing, the leg begins to act as a kind of pendulum, and remember that the pendulum is directly proportional to the length, that is,
In this way, by bringing their legs closer they reduce the distance and make the period shorter.