Question

(4) Abdi has two electric train sets: A and B. Each train is on its own circular track. He starts both trains at the same time. Train A returns to its starting point every 12 seconds. Train B returns to its starting point every 9 seconds. If the trains continue traveling, what is the least amount of time, in seconds, that both trains will arrive at the starting points at the same time?

Answer 1

The least amount of time both trains will arrive at the starting points at the same time is 36 seconds.

Explanation:

From the question, Train A returns to its starting point every 12 seconds and Train B returns to its starting point every 9 seconds.

First, we will determine the times the trains will return to the their starting points.

For Train A,

The second time Train A will return to its starting point will be at 24 seconds,

The third time will be at 36 seconds

The fourth time will be at 48 seconds and so on.

For Train B,

The second time Train B will return to its starting point will be at 18 seconds,

The third time will be at 27 seconds

The forth time will be at 36 seconds and so on.

Since both trains arrive at their starting points at 36 seconds,

Hence, the least amount of time both trains will arrive at the starting points at the same time is 36 seconds.