A: It’s unusual to not have enough hot water with a gas water heater, since they tend to either work or not work — there’s usually plenty of hot water or virtually none at all.
Before undertaking the expense of a new water heater, I would first talk with the utility company that supplies the gas, and have them come out and check the incoming gas pressure and the condition of the burner. Low pressure or a partially clogged burner can cause the problem. I would also suggest shutting the gas, then draining the tank and flushing it with fresh water to remove any sediment.
You might also be having a problem with the dip tube. That’s a plastic tube that sits inside the tank on the cold water side, and directs the incoming cold water down to the bottom of the tank to be heated. If the dip tube cracks or deteriorates, it allows cold water to remain at or near the top of the tank, where it doesn’t have time to get sufficiently heated. You can sometimes — but not always — recognize this problem by the presence of tiny bits of white or gray plastic in the faucet strainers. Replacement dip tubes are available at most home centers and other stores that specialize in retail plumbing parts.
If all that is OK, then the problem is probably one of capacity. A 15-minute shower is pretty long, and will go through a lot of hot water. You could consider low-flow shower heads, or replace your existing water heater with one that has a larger capacity.