OK then.
Assuming it survives long enough, a 120V kettle run on 240V will boil in less than a quarter of the time. [Note 'quarter', not 'half', as twice the voltage will provide four times the power.]
Conversely, a 240V kettle run on 120V will take more than four times the normal time to boil. In fact, it literally could take forever to boil. I know this to be true as I once took a single-voltage UK travel kettle on a holiday in the USA!
These apparent anomalies are because, unless it's perfectly insulated, as a kettle heats up it will radiate more and more heat.
Consider the case of the 240V kettle on a 120V supply. The rate of heat radiation eventually may balance the rate of electrical input, so a state of equilibrium is reached before the kettle boils. No matter how long you leave it (or even watch it), it will never boil. It's therefore a pretty good guess that, on a 240V supply, a 120V kettle will boil in less than half the time.
BTW, for my next trip to the USA, I made sure that I took a dual voltage kettle. I can confidently report that, when on the correct voltage setting, it seemed to boil just as quickly as it had done in the UK.