How many months does it take to fly to Mars?

How to get close to this number

The distance is the wrong starting point; the orbit is the right one. A spacecraft does not fly in a straight line to Mars, it enters an elliptical transfer orbit around the Sun and coasts most of the way, arriving where Mars will be rather than where it is. That path is roughly half a solar orbit of the transfer ellipse, which sets the duration at a substantial fraction of a year regardless of how fast the rocket is.

Most people underestimate because they divide distance by speed. That works for a car and not for a spacecraft, which spends almost the entire journey with its engines off. Fuel buys a shorter trip only at steeply increasing cost, so mission planners take the slow efficient path — which means the travel time is set by orbital mechanics, not by engineering ambition.

The constraint the question does not mention is the one that dominates a crewed mission. As the explanation says, launch windows open only when the planets align, and a crew that arrives must then wait for the return window. The journey is measured in months; the mission is measured in years, and confusing the two is the most common misreading of this figure.