Electrical machines designed for 50Hz can usually work safely in 60Hz power supply, but not applicable to 60Hz machines to be run in 50Hz power supply. This is because impedance of 50Hz machines increases if operate in 60Hz supply which also lowers the running ampere, while if 60Hz machine run in 50Hz power system will experience increase in running ampere & overheating that will result to reduced life expectancy of the equipment. In motors coupled to water pumps or compressors increase of rpm will tend to increase current but you can lower the voltage down slightly below the nameplate value to compensate.
Motors nominal operating voltage is stated in the nameplate. Most China made washing machines are rated at 380V 50Hz, but are being run at 415 or 440V power grid in other countries outside China. Most motors with nominal voltage of 440V are also working at 380V in country with this generating standard. So it is always the choice of the owner which way he wishes to follow. In my experience in ship building industry as electrical commissioning engineer, sometimes we are faced with some technical issue regarding rated frequency especially in water pumps. It is not always easy to just change the machine or equipment to rated frequency considering the FINANCIAL BURDEN that comes with it.
In 50 cycle centrifugal pumps connected to 60 cycle power supply in order to reduce the increased of current due to increase in rpm the flow of fluid to the pump will be reduced. The rate of flow will be reduced and so thus the current taken by the motor driving the pump. In power generation, lowering the voltage of the system doesn't result in increase of ampere taken by the loads. The ampere of the system lowers down as voltage go down because the overall impedance of the system is the same and lowering the voltage doesn't lowers the impedance. In motors this principle is also the same, not unless you lower the voltage too much.
Lowering the voltage will lower the current drawn as long as the load is purely resistive. In case of loads like motors, lowering the voltage will result in increase of current since the motor still tries to run almost at synchronous speed (with slip). To generate this torque at this reduced flux due to lowering of voltage, this will be seen as increased current drawn by the motor. It is also not advisable to run motors at 20% over speed unless the motor is rated for such a duty. So in this case, GoHz frequency converters would be the best bet to make it work perfect.