The water boiling one doesn't make any sense. One of those devices (stove or kettle) transfers more heat per unit of time into the water. Just use that device for the full amount of water.
An induction range would remove the need for transferring boiling water around. At least in the US, that's the fastest device, since countertop kettles are limited to 1.8kW or so. Induction 'burners' usually are 2.5-4kW, and assuming the right cookware, much better at transferring that energy into the water (and not the air like a gas burner)
> One of those devices (stove or kettle) transfers more heat per unit of time into the water. Just use that device for the full amount of water.
I think you're missing the part where you dump one into the other once one boils.
Obviously, heating in parallel is going to be faster.
Heating a cup of water each in two different kettles is faster than heating two cups of water in only one kettle.
Related Technology Connections video, where he uses electric kettle at 6 kW, to boil 1L of water in 55 seconds: https://www.youtube.com/watch?v=INZybkX8tLI
Fastest way to do it: induction hob and a hot water tap with one of those under sink boilers. It takes longer to fill the pan than to get the water to a rolling boil.
> One of those devices (stove or kettle) transfers more heat per unit of time into the water. Just use that device for the full amount of water.
But.. Applying heat from two sources is better than applying heat from only one?