If patricia drives at two-third of her usual speed, she covers a certain distance in one hour more than the time she takes while driving at her usual speed. the time taken by her to cover this distance with her usual speed is hours. me!

Let r = usual driving rate
let t = usual driving time
We need to figure out t

The distance she covers in her usual time at her usual rate is r*t

The distance she covers in her new time at her new rate is:
(1+t)*((2/3)r)

Set this equal to each other and solve for t.

rt = (2/3)r + (2/3)rt
(1/3)rt = (2/3)r
(1/3)t = (2/3)
t = 2

So her usual time is 2 hours. (There's probably a faster way to do this)