Problem Solving

This is a relatively easy OG work rate problem. But I am trying to follow the RTD table technique suggested by Manhattan GMAT. I am not able to reach a solution using that technique for this question.

The question is #223 in OG 11th edition Problem Solving section (page 182)

Car A is 20 miles behind car B, which is traveling in the same direction along the same route as car A. Car A is traveling at a constant speed of 58 miles per hour and car B is traveling at a constant speed of 50 miles per hour. How many hours will it take for car A to overtake and drive 8 miles ahead of car B?

The easy solution is to find the relative speed and the extra distance traveled by car A to figure out the time taken to catch up with Car B.

But I am trying to learn the manhattan GMAT RTD table technique and I want to make sure this technique works for this problem

A B
---------------------------------------
Rate 58 50

Time ( T + 28/58 ) T

Distance ( X + 28 ) X

I basically come up with two equations here. The first one for car B :
X = 50T

The second equation for car A : 58*( T + 28/58 ) = X + 28. I substitute for X and solve for T in the second equation.

But this method does not yield the right answer. Why? Anybody familiar with this technique? Your help is much appreciated.

Thanks in advance.