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