Final answer:
The buses that leave at 6 am with intervals of 35 and 50 minutes will next arrive together at the bus stop at 11:50 am. This is determined by finding the Least Common Multiple (LCM) of 35 and 50, which is 350 minutes.
Step-by-step explanation:
To determine when two buses that have different return intervals will arrive at the bus stop at the same time, we need to find a common multiple of the two time intervals. The first bus returns every 35 minutes, and the second bus returns every 50 minutes. To find a time when both buses will return to the bus stop simultaneously, we can use the Least Common Multiple (LCM) of 35 and 50.
Step 1: List the multiples of each number until we find a common one:
- Multiples of 35: 35, 70, 105, 140, 175, 210, 245, 280, ...
- Multiples of 50: 50, 100, 150, 200, 250, 300, ...
Step 2: Identify the smallest multiple that is common to both lists. The LCM of 35 and 50 is 350 minutes.
Step 3: Convert the LCM from minutes to hours and minutes. There are 60 minutes in an hour, so 350 minutes is equal to 5 hours and 50 minutes.
Since the buses leave the stop at 6 am, and the LCM is 5 hours and 50 minutes later, the buses will next arrive together at the bus stop at 11:50 am.