re: Hot water from the tap, do you use it to cook?

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cold water would boil faster

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Physics tells us this is wrong, but many people persist in believing "alternate facts". Another is that previously-boiled water freezes faster. A popular belief is that water in altered physical states can have special health benefits. You can buy devices with the promise of generating such special water...save your money.

Ironically, physics or confusion about physics is behind some of these beliefs. Liquid water is a mix of molecular chains shifting among configurations in a small fraction of a second. Different mixtures can have slightly different properties. For unusual mixtures to persist requires highly modified experimental environments.

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Another is that previously-boiled water freezes faster. A popular belief is that water in altered physical states can have special health benefits.

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This may have nothing to do with your post, but i've seen some videos on how to get crystal clear ice cubes. From the internet, apparently, the reason ice isn't "factory clear" is because of the dissolved oxygen in the water. By boiling the water, then freezing, and repeating that process, you release the oxygen during the boil.

I've never tried it because that's too much trouble to make fancy ice, but if i'm bored enough, i may give it ago for my whiskey balls.

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I once worked with a guy who swore that putting hot water in an ice cube tray would freeze faster than cold tap water.

I looked at this idiot like he had 2 heads, and both of them were on backwards.

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He is actually almost right and might be what the science teacher in question was really talking about.

IIRC the break over is 140F. Water at or warmer than ~140F actually freezes slower than 212F water. It is a result of rapid vaporization at higher temperatures. There are a lot of caveats like it is more pronounced with larger (but equal) surface areas. I am too lazy to go into a full explanation but should be an easy google search. If you have ever seen the videos of people in super cold areas throwing hot water into the air and it freezing immediately you have seen this effect.

Again to the guy this is a response to cold water always take longer to heat with mass, surface area, conductivity, heat introduced, and etc. There is no chicanery going up like there can be coming down.