Does a traveller’s increasing speed shorten the time interval or slow down the clock?

This paper examines a familiar physical scenario in the context of relativity: a person walking on a moving conveyor belt in an effort to catch his airplane – a situation that inherently involves principles of relative motion. According to both the Lorentz transformation and the currently accepted form of the Galilean transformation, the motion of the conveyor belt provides no net advantage to the walker. In contrast, both practical human experience and AI-generated reasoning consistently affirm that the conveyor does, in fact, assist the walker in reaching the plane more quickly. This discrepancy – between formal relativistic mathematics and observable physical outcomes – raises important questions about the completeness and contextual applicability of existing theoretical models. As a proposed resolution, this paper brings again a recently introduced mathematical formalism: a modified transformation derived from the Galilean framework, extended to remain valid across all contexts involving relative motion. Grounded in analytical reasoning and supported by a coherent geometric interpretation, this approach aims to reconcile theoretical predictions with everyday empirical realities. In the end, it has been found that, in explaining time relativity, when a traveller increases his speed while covering a distance, it is not his clock that runs more slowly, but rather the time interval required to cover the distance becomes shorter.