Question

Sea-tac Alrport in Seattle. WA, has a flight leaving for Dallas, TX every 2 hours and a flight leaving for Washington, D.C. every 45 minutes. At 5:00 A.M. on Monday, a flight to Dallas and a flight to Washington, D.C. leave at the same time. What is the next time that flights to Dallas and Washington. D.C. will leave at the same time?

Answer 1

The flights to Dallas and Washington D.C. will leave at the same time again at 11:00 A.M. on the same day, after finding the least common multiple of their departure intervals which is 360 minutes or 6 hours.

Step-by-step explanation:

To find when both flights will leave at the same time again, we need to look for a common multiple of their departure intervals. The flight to Dallas departs every 2 hours (120 minutes) and the flight to Washington D.C. leaves every 45 minutes. To find the least common multiple (LCM) of these two intervals, we can list the multiples of each until we find a common value.

1. Multiples of 120 minutes: 120, 240, 360, 480, 600, ...
2. Multiples of 45 minutes: 45, 90, 135, 180, 225, 270, 315, 360, ...

We see that the least common multiple is 360 minutes, which is 6 hours. Since the initial flights leave at 5:00 A.M., the next time both flights will leave together is 6 hours later, which is 11:00 A.M. on the same day.