Slow and steady wins the race

Algebra Level 2

A HARE AND A TORTOISE RACE ON A CIRCULAR TRACK OF RADIUS 50m. THEY BOTH START FROM THE SAME POINT BUT RUN IN OPPOSITE DIRECTIONS (CLOCKWISE AND COUNTER CLOCKWISE). THE FIRST ONE TO COMPLETE A FULL CIRCLE AND RETURN TO THE STARTING POINT WINS. ALSO, IT IS GIVEN THAT:

1)THE HARE STARTS RUNNING WHEN THE TORTOISE HAS ALREADY COVERED 1/5th OF THE DISTANCE.

2)THE HARE MEETS THE TORTOISE ON THE TRACK WHEN THE HARE HAS RUN 1/8th OF THE DISTANCE IN HIS DIRECTION.

BY WHAT FACTOR SHOULD THE HARE INCREASE ITS SPEED AFTER MEETING THE TORTOISE IF IT HOPES TO END THE RACE IN A TIE???

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