5/6 hours

**Explanation : **
Let's call the amount of fuel in each car as "x".
Tony Stewart's car can drive for 4 hours with x amount of fuel, so his fuel consumption rate is x/4.
Jamie Mcmurray's car can drive for 5 hours with x amount of fuel, so his fuel consumption rate is x/5.
After a certain amount of time, they realize that the amount of fuel in Tony's car is 1/4th of the fuel in Jamie's car. So, x/4 = x/5 * 1/4.
Solving for x, we get x = 20.
So the amount of fuel in each car is 20.
Now, we can use the fuel consumption rate of each car to find out how long they have been racing.
Let's call the time they have been racing as "t".
Tony's car has x - x/4 * t = 20 - 20/4 * t = 20 - 5t amount of fuel left.
And Jamie's car has x - x/5 * t = 20 - 20/5 * t = 20 - 4t amount of fuel left.
We know that Tony's car has 1/4th of the fuel left in Jamie's car, so:
20 - 5t = (1/4) * (20 - 4t)
Expanding and simplifying, we get:
20 - 5t = 5 - t
25 - 6t = 5
t = 5/6 hours.
So, they have been racing for 5/6 hours.