Very accurate simulation, I can fully relate to this experience. It could be made even worse by adding a "single hot water tank" mechanic that makes the water turn cold suddenly as soon as someone pull some water from the kitchen :P Or the hard mode with an old boiler that needs a very strong initial pressure to even get started heating up the water </true story>.
I tried my best but couldn't manage to get showered in time though, balancing heat and cold is doable, but even with good temperature levels I've never seen the "cleanliness" bar advance faster than the "time" one...