Help with hotwater tank setup.

I recently moved into an apartment, that has Gas hotwater. Annoying extra bill to pay. Anyway its just me and my partner so we have pretty low hotwater use, but we find our hotwater pressure frequently drops. I had a chance to access my hotwater tank and have attached a few pics. To me it seems the tank on the right(the tank I pay for) is feeding hotwater to the tank on the left. (The tank that supplies the landlords much larger house) Therefore it would seem like my tank is doing all the work and im paying for it. Anyway I want to be sure before I approach my landlord. Thanks for any help.

Hard to tell from these pics.
It looks like the cold water supplies, which have lever handle valves, are connected together.

I don’t see any connection between the hot water piping.
Yours looks 1/2 inch, his looks 3/4 inch.

But it could be joined up somewhere over on the left, or somewhere else.

Just ask him about it without accusing.

Your hot pressure would also drop if he is using hot or cold water, but might feel hotter after awhile.

Whatever water he used will reduce your overall pressure, since you are on the same supply source of incoming water.

If it comes down to proof, ask him if he will turn off both heaters, wait three hours, then just light yours.
Wait another half hour.
If he gets hot water, or very warm water, he is mooching your hot water.

I pretty much agree with Jeff's take on this.
Your tank is not feeding into the other tank as you suspected.
The hot water line from your tank IS NOT shown feeding into the tank on left. A hand on the hot water line from your tank would confirm that.

As far as the 2 hot water lines joining together further downstream, that's a possibility but shouldn't be the case. Follow your HW line as far as you can.
If they were connected somewhere downstream, one way to help confirm or deny it, would be to temporarily shut the CW line into your tank and if that stopped your HW to your fixtures, that should indicate that there was no downstream interconnection.

It appears both hot water outlets from the tanks are 1/2''
the tank on the left reduces at the ball valve

how big is his house? how many baths?
how many baths in your house?
you have a 3/4 cold feeding 2 houses.
and 1/2'' hot feeding both houses
you will experience a drop in pressure in your house when he uses water in his house

hot water line is under sized

frodo, good eyes, I missed that step down on the hot line of the owner’s tank.

Diehard, good test idea!

Unless the owner is a jerk, and has a check valve so he can only steal hot water, and not share any going the other way.

But very unlikely.

Just follow your hot water piping and see where it goes too. If it just goes to your fixtures then your using more than
you think. If the piping disappears then it might be going to your landlords fixtures.

I can't imagine landlord stealing hot water; extra "income" per month too low to bother.
Raising rent an additional $10/mo wouldn't scare off a tenant, and would reap a bigger amount.