The Hike Time Calculator is designed to estimate the total time required for a hiking or backpacking trip by taking into account the distance hiked, elevation gain, and the physical toll of the trek including fatigue and rest breaks. It provides a comprehensive view by combining the time taken to traverse the distance at an average set speed, the additional time needed to overcome elevation gains at half the ascent rate due to the difficulty of climbing, an increase in time for each mile hiked based on a fatigue factor, and the cumulative duration of rest breaks.