To understand this question, let’s create some Mathematical examples to illustrate the question.
First, we know that slope is the ratio of the change in y over the change in x, or more commonly known as rise over run. Remember, a ratio is a comparison between two quantities. So, let’s view the slope as a ratio. Since the scenario is climbing a hill, we can use the ratio of elevation gained per minute as the slope.
Slope: elevation (ft.)/minute
This would mean that a slope of 4/4 is 4 feet gained per 4 minutes, which simplifies to 1 feet gained per minute. A slope of 1/3 would mean 1 foot gained per 3 minutes. Consequently, you have two options: you can gain 1 foot per minute or 1 foot per 3 minutes. If you were to climb at 1 foot per minute, you would summit the hill in less time (1/3 of the time it would take to climb the 1/3 slope); however, this is a steeper slope and would require more energy. If you were to climb the hill at 1 foot per 3 minutes, you would ascend the hill 3 times longer than the 1 foot per minute slope; however, you would use less energy at the summit.
So, this is up to you: would you rather climb in 1/3 if the time but used a majority (or all) of your energy, or would you rather climb the hill 3 times longer but have energy remaining?