Answer :
Final answer:
The next time when all three lights will flash together is 8:28 p.m.
Explanation:
The three lights flash at intervals of 2 minutes, 3.5 minutes, and 4 minutes. To find the next time when all three lights will flash together, we need to find the least common multiple (LCM) of these intervals.
The prime factorization of 2 is 2.
The prime factorization of 3.5 is 3.5 = 2 * 1.75 = 2 * 7/4 = 2 * 7/2 * 1/2 = 2 * 7/2 * 2/2 = 2 * 7/2.
The prime factorization of 4 is 2 * 2.
Therefore, the LCM of 2 minutes, 3.5 minutes, and 4 minutes is 2 * 7/2 * 2 = 28 minutes. So the next time when all three lights will flash together is 28 minutes after 8 p.m., which is 8:28 p.m.
