Final answer:
To qualify for a marathon, a runner must complete another race in no more than 210 minutes, represented by the inequality t ≤ 210. Runners who take longer than 210 minutes do not qualify, as indicated by the inequality t > 210.
Step-by-step explanation:
To qualify for a certain marathon, a runner must complete a different marathon in no more than 210 minutes. The inequality representing the time in minutes t that would qualify a runner for the marathon is t ≤ 210. This means any time that is less than or equal to 210 minutes is acceptable for qualification.
Conversely, the inequality representing the time in minutes that would not qualify a runner for the marathon is t > 210. In this case, any time greater than 210 minutes would be deemed too long for qualification purposes.
Explanation for Qualifying Time
Marathon races are generally measured by how quickly they can be completed, with shorter times being more desirable. This is why a qualifying time is set as a maximum limit; it establishes a standard for participants to meet or exceed in order to take part in the event.
Non-Qualifying Time Explanation
Those who do not qualify either did not participate in the required preliminary marathon or exceeded the maximum time limit, thereby not meeting the established standards for this particular race. In this context, having a non-qualifying time means being unable to participate in the event due to not meeting the race criteria.