Question

The train that goes to the south zone has a frequency of 5 minutes and the one that goes to the north zone 3 minutes. At 8 in the morning, a train leaves for each area. How many times will the two trains leave together between 8 and 10 am? At what times will it happen?

A. Once at 8:15 am
B. Twice at 8:20 am and 9:00 am
C. Thrice at 8:30 am, 9:15 am, and 9:45 am
D. Four times at 8:45 am, 9:30 am, 9:55 am, and 10:00 am

Answer 1

The two trains will leave together 8 times between 8 and 10 am, at 8:00 am, 8:15 am, 8:30 am, 8:45 am, 9:00 am, 9:15 am, 9:30 am, and 9:45 am.

Step-by-step explanation:

To find out how many times the two trains leave together between 8 and 10 am, we need to determine the time interval when both trains depart at the same time. The two trains have frequencies of 5 minutes and 3 minutes respectively, which means that they will align every 15 minutes (the least common multiple of 5 and 3). Therefore, the two trains will leave together every 15 minutes. Between 8 and 10 am, there are 120 minutes in total. Dividing 120 by 15 gives us 8. Hence, the two trains will leave together 8 times between 8 and 10 am. The times when it will happen are 8:00 am, 8:15 am, 8:30 am, 8:45 am, 9:00 am, 9:15 am, 9:30 am, and 9:45 am. Therefore, the correct answer is option C: Thrice at 8:30 am, 9:15 am, and 9:45 am.