Tranny Problems

I took my car up to the local track this past weekend for a test and tune and when I was racing the transmission took a long time to shift. I was manually shifting my automatic and I would shift and it would be awhile before my car would shift. It did this more on the 1-2 shift then on the 2-3 shift. The 2-3 shift it would do it but it didn't take quite as long. I know it is going to need some work but what is the most likely cause of this?

Another question I have is what is the most likely gear ratio to come in a 73 Duster with a 318. I have looked at many ratio calculators and it doesn't ever come up with anything close to a ratio I have ever heard of. I do have bigger tires on the back then original but I put in that tire height and I get weird ratios.

Thanks