Answer: Cat will win the game as Cat was the fastest between the two.
Explanation:
Let the number of steps of dog be n
Let the number of steps of cats be 1.3n
Let Distance of each step of cat be x 
Let distance of each step of dog be 0.7x
According to question, 
Total distance covered by dog be 

Total distance covered by cat be 

As we can see that 

Hence, Cat will win the game as Cat was the fastest between the two.