Final answer:
Allison and Sameer run together for the first time on September 18 (option B) and will run together again on October 3 (option D).
Step-by-step explanation:
Allison runs every 3 days starting on September 3, and Sameer runs every 5 days starting on September 5. To figure out when they run together for the first time, we need to find a common multiple of 3 and 5 that would represent the days passed since their respective starting points. The least common multiple (LCM) of 3 and 5 is 15. Counting 15 days from each of their starting dates, we find that they run together for the first time on September 18th (15 days after September 3) and September 20th (15 days after September 5), but the first common day is September 18th, which is option B. To determine when they run together again, we would look for the next common multiple of 3 and 5 after 15, which is 30. Adding another 15 days to September 18 gives us October 3. Thus, they will run together again on October 3, option D.