The time it takes to travel to Mars using a nuclear fuel-based engine depends on various factors, such as the type of nuclear propulsion system, the specific engine design, the spacecraft's mass, and the orbital positions of Earth and Mars at the time of the mission.

Two common types of nuclear propulsion systems that have been proposed for space travel are Nuclear Thermal Propulsion (NTP) and Nuclear Electric Propulsion (NEP).

Nuclear Thermal Propulsion (NTP) systems work by using a nuclear reactor to heat a propellant, usually hydrogen, which is then expelled out of the engine to produce thrust. NTP systems could potentially reduce the travel time to Mars from the 6-8 months required by conventional chemical rockets to around 3-4 months.

Nuclear Electric Propulsion (NEP) systems generate electricity from a nuclear reactor, which is then used to power ion or plasma thrusters. While NEP systems are more fuel-efficient than NTP, they typically generate lower thrust, which could result in longer trip durations. However, continuous acceleration offered by NEP systems might still enable travel times of around 6 months or less, depending on the spacecraft design and mission parameters.
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