What kind of tea do you boil for 45minutes?

Chai masala variants may be boiled that long or more – they do contain black tea, but also spices (where the boiling is needed, to extract the flavor from whole spices). The tea decoction this produces does contain all of the bitter compounds, sure – but it is mixed with spices, diluted generously with milk and sugar, and becomes a palatable drink that is nevertheless very different from the coolly and weakly brewed variety you seem to be familiar with.

In fact, it is even possible that the tea was plain black tea, brewed very strongly. Served with plenty of milk and sugar to balance the bitterness, milk tea is a cultural variation. Think of it kinda like coffee, if you want – it is bitter, but it is expected to be – and the tea can be doctored to make it work for the drinker.

Tea can be served in lots of different variations, and none are more correct than others – just like some teas are brewed very light and almost flavorless (japanese green, and 15 seconds per brew), and others are brewed to death and sweetened to balance (southern style sweet tea), some are served with milk, sugar, or lemon, and still more are served with salt or butter (tibetan). Boiled milk tea or chai are brewed to death, to extract all the flavor, and served sweet and milky to balance the strength and bitterness – and a weakly brewed tea would be tasteless and vanish in the expected fixings.

You mention samovar. That is kind of predecessor of electric kettle, that can not only boil water, but can keep it hot afterwards too.

To make tea with it, one would first brew a very strong tea concentrate. Then each guest would repeatedly pour a little of that in their cup, dilute it with hot water from the samovar and drink it sweetened, usually with caramel.

The concentrate would be really very strong and bitter and might have easily been boiled for 45 minutes.

It's in fact not that strange to boil tea, as this was how it was originally prepared thousands of years ago by the Chinese. Boiling indeed results in a bitter brew, but at that time it was mainly for medicinal purposes.

Even today, you can visit Tibet and other nearby regions, you still see people boiling black or pu erh tea. The locals love a very strong brew and hot brew. In the cool climate there, people love it. It keeps them warm. I have to say though that mostly when I see people boiling tea leaves, they do add other flavoring. The tibetans add yak milk and sweeteners. See more here on WikiPedia: butter tea

Before going too much off topic ;) Generally the more 'oxidized' teas are more suitable for boiling (if you really want that). Green teas are minimally oxidized, so you end up with something pretty grassy and bitter. Black teas are better. Pu erh teas, especially ripe/shou pu erh are post fermented and won't taste bitter even after boiling.

What's typically also more suitable for boiling are crushed teas. The purpose of boiling is to as much as flavor as possible, and with crushed leaves more leaf is in contact with water (compared to full leaf or bud teas).