To solve this problem, we need to find out how many freshmen and sophomores are at the rally at 1 p.m. Let's start by calculating the number of freshmen who arrive at the rally after 12 p.m.:
20 freshmen arrive every 5 minutes, which is equivalent to 4 freshmen per minute.
Between noon and 1 p.m., there are 60 minutes, so the number of freshmen who arrive during this time is:
60 minutes x 4 freshmen/minute = 240 freshmen
Now let's calculate the number of sophomores who leave the rally after 12 p.m.:
15 sophomores leave every 5 minutes, which is equivalent to 3 sophomores per minute.
Between noon and 1 p.m., there are 60 minutes, so the number of sophomores who leave during this time is:
60 minutes x 3 sophomores/minute = 180 sophomores
Therefore, at 1 p.m., the number of freshmen at the rally is:
1,200 + 240 = 1,440 freshmen
And the number of sophomores at the rally is:
1,500 - 180 = 1,320 sophomores
The ratio of freshmen to sophomores at 1 p.m. is:
1,440/1,320 = 120/110
Simplifying this fraction by dividing both the numerator and denominator by 10, we get:
12/11
Therefore, the ratio of freshmen to sophomores at 1 p.m. is 12/11.