Two trains are running, on separate tracks, round a model railway layout. One completes a circuit every 40 seconds and the other every 55seconds. The trains start together at the station. How long, in minutes and seconds, will it be before they are at the tation together again?
well,
40 = 5*8
55 = 5*11
To find out how long it will be before the two trains are back at the station together, we need to find the least common multiple (LCM) of their individual times for completing a circuit.
The first train completes a circuit every 40 seconds, and the second train completes a circuit every 55 seconds.
To find the LCM, we can list the multiples of each train's time until we find a common multiple.
Multiples of 40 seconds: 40, 80, 120, 160, 200, 240, 280, 320, 360, 400, ...
Multiples of 55 seconds: 55, 110, 165, 220, 275, 330, 385, 440, 495, 550, ...
From the listed multiples, we can see that the first common multiple is 440 seconds.
Now, we convert 440 seconds into minutes and seconds:
1 minute = 60 seconds
440 seconds = 7 minutes and 20 seconds
Therefore, it will be 7 minutes and 20 seconds before the two trains are back at the station together.