Two model trains begin at the toy train station and travel continuously on two circular tracks of equal length. The first train completes a circuit in 20 seconds and the second train in 15 seconds. If both trains, leave the station at the same time, after how many seconds will the two trains first meet again?
Answer is 60 seconds, but I don't know did they get it. Please show me the calculation please. Thanks
20 = 4*5
15 = 3*5
LCM(15,20) = 3*4*5 = 60
every 60 seconds one train does 3 laps, and other does 4 laps.
To find out when the two trains will first meet again, we need to determine the time it takes for both trains to complete an integral number of circuits. Since the first train completes a circuit in 20 seconds and the second train completes a circuit in 15 seconds, we need to find the smallest common multiple of these two numbers.
To do this, we can start by listing the multiples of the two numbers:
Multiples of 20: 20, 40, 60, 80, 100, 120, ...
Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, ...
From this list, we see that the two trains will first meet after 60 seconds when both trains complete 3 circuits. Therefore, the two trains will first meet again after 60 seconds.