One model train travels around a loop every 5 minutes. The other travels on anothe loop every 4 minutes. If they begin at the same point at the same time, how much time will pass before they meet at that point again?
The rate for the first is one loop per 5min, the other one loop per four minutes. The combined rate is the sum of these:
1loop= (lloop/5min + 1loop/4min)*time
time= 1/(1/5 + 1/4) minutes
This is somewhat tricky to get combined, if you wish, you can make decimas..
time= 1/(.2+.25)= 1/.45 and you take it from there.
200,000=?thousands ? ten thousands ? hundred thousands
time= 1/.45= 2.2 seconds.
oops..time= 2.2 minutes.
To determine how much time will pass before the two model trains meet at the starting point again, we need to find the least common multiple (LCM) of their time periods.
The first train goes around the loop every 5 minutes, while the second train completes its loop every 4 minutes.
To find the LCM of 5 and 4, let's list the multiples and look for the smallest common number:
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, ...
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, ...
From the lists above, we can see that the smallest common number is 20. Therefore, the two trains will meet at the starting point again after 20 minutes.
So, the answer is that 20 minutes will pass before the two model trains meet at the starting point again.