I cover a certain distance in 3 hours. If my speed increases by 1/3, why is my travel time not also reduced by 1/3 (so travel the same distance in 2 hours)?

t  =  2.25 h

Step-by-step explanation:

In the case, I cover distance d in 3 hours

d =  3 * v₁      (1)

In the second case my speed increase by 1/3 then my speed is  

v₁ + (1/3) v₁   =  (3/3  + 1/3  ) *v₁

my new speed is   (4/3) * v₁  and

d  =  (4/3)*v₁ * t    (2)

Dividing (2) by  (1)  we get

1   = (4/3) *v₁*t/ 3*v₁

1  =  (4/9)*t

t = 9/4  h

t  =  2.25 h

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