Bathtime puzzler

[hunt_the_fox]

Gents,

I was wondering if you could help shed some light on a Hunt household phenomenon.

When I have a bath if I turn both taps on full and leave the water when the level reaches the overflow the hot water will have run out and I will have a tepid bath.

But if I fill the bath 1/4 full of hot water then 1/2 with cold water and then top up with hot water I can reach the same level but with a piping hot bath. Now given there is the same finite amount of hot water being used to fill the bath how does it mean that I get a hot bath when using the water in the latter way but not the former? I am confused.

HTF.

[hunt_the_fox]

Smart roadster said:

During the bit when you are only filling the bath with cold, the water in the hot tank has a chance to heat up again.

I thought that but it seems to work even when neither the immersion heater nor the timed boiler are on.