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Volts don't measure power. Also nobody specified the load was resistive. Most loads are not resistive. See light bulbs, diodes (inc. LEDs) and even electric motors as an example. If you are talking about resistive loads you need to specify that. For a resistive load doubling the potential difference (volts) causes the current to also double because I = V / R and power to quadruple P = VI. So run time would half since you are spending double the energy at four times the power (power is rate of energy consumption).

I am now disappointed in people who call themselves electricians.