In a $100$ meter track event, alice runs at a constant speed and crosses the finish

10s

Explanation:

If it took Beatrice 25 seconds to complete the race

Distance = 100 meter

Beatrice speed = 100/25

                          = 4m/s

If Alice runs at a constant speed and crosses the finish line $5$ seconds, she must have completed the race in 20s (25 -5).

Her speed where constant

= 100/20

= 5 m/s

It would take Alice

= 50/5

= 10s

It would take Alice 10s to run $50$ meters.

To solve this problem it is necessary to apply the equations related to the time measured from a relative viewer and the mathematical equations of motion.

Speed is defined as

Where,

d = Distance

t = Time

Re-arrange to find d,

Applying the equations of relativity of time,

Where,

v = Velocity

c = speed of light

Reference time

t = relative time

Replacing,

Therefore the distance would be

Therefore the travel will be 5.5Km