Water Heaters - Will larger water heater increase hot water time?

I'm a first-time homebuyer, just recently bought a 900 sq ft condo.
There are two bathrooms - one right next to the water heater room and one on the opposite side of the apartment. The shower closest to it gets hot water in less than a minute, but the shower on the other side of the apt. takes maybe 5 minutes before the water turns hot. The pressure is very good so I don't think there's anything clogging the pipes.
The water heater is a 30 gal A.O. Smith which is over 12 years old and only gives hot water when the thermostat is set to 'Very Hot', which, I thought, shouldn't be necessary. I called A.O.Smith and they told me that over time the thermostat core can wear out and so I should replace it eventually, even though it hasn't started leaking and still gives hot water.
My question is: if I got a larger unit - say 40 gal or 50 gal - would that make the water turn hot faster for the shower that's further away? Or is it simply the age of this unit which causes it to take so long to heat water a moderate distance away?

Thanks in advance for any info!

No, larger won't make the water at the faucet get hot quicker. It will allow you to have hot water longer though. If its really a full 5 min, that seems excessive, but it depends on where and how the pipes are routed.

You could have a bad thermostat or heating element. At 12 y/o, its pretty much at the end of its useful life.

Make sure you have enough space for the new one..check diameter and height.

It probably shouldn't take so long to get hot water. You probably have a plumbing defect that should be identified and repaired.

One possibility would be a water mixing valve that is allowing cold water to contaminate the hot water system, keeping the water cool.

Shower valves are typically mixing valves these days.

To test this theory, turn the water off to the water heater. Then turn the shower valves to supply hot water. The water should stop flowing quickly when the water is turned on. If you get a constant flow of cold water coming out of the shower head, you have a problem.

You should test all the mixing valves for this kind of problem, including the washing machine and kitchen sink. A problem could be on any of these valves.

when you open the hot water no matter where the bathrooms are the pressure your seeing on the hot water is the cold water going into the HWH to replace the hot water going out.insulating of the longest run will keep the heated water better going to that distance bath...anything along the run lower in temp of the hot water water will pull on the delivery temps you probably see a big difference in the winter with the wind blowing.

A 900 sq.ft. condo?? There's no way it's going to take 5 minutes for the water in the bathroom to get hot, UNLESS you are talking about the lavy valve, and the aerator is so clogged that you barely get any water through it. (Or the shower head is so clogged that it's the same situation.)

You only get hot water when the valve on the WH is set to "Very Hot" -- the thermostat (or gas valve, if it's gas) needs to be replaced.