Final answer:
Solving for time in physics or math often results in both positive and negative values. However, negative values can be disregarded in real-world contexts since they would imply an event happening before the start, which is not possible. Therefore, in the scenario of Riko and Yuto, only the positive time value when Riko catches up to Yuto is considered valid. Option c.
Step-by-step explanation:
When solving for time in physics or mathematics, situations may arise where the solution yields both a positive and negative value. In the context of this problem, Riko catching up to Yuto after a certain period, we are dealing with a scenario where time must represent a point from the start of an event. As such, t = 0 corresponds to the moment when Riko leaves her house, and this indicates the beginning of the event measured.
In the given examples, the times t = 3.96 seconds and t = 10.0 seconds are reasonable as they represent times after the start of motion. However, negative times like t = -1.03 seconds and t = -20.0 seconds suggest events occurring before the start, which is not possible within this real-world context. Therefore, these negative time values are disregarded.
Hence, it's concluded that Riko will be behind Yuto from the time she leaves her house (t = 0) until she catches up after 52.5 minutes. Since negative times are not plausible in this scenario, they are considered invalid, reinforcing the concept that time cannot be negative option c, in real events.