Two soldiers are guarding a building. In the diagram shown, the first soldier starts at S, and walks around the building once every 20 minutes. The second soldier starts at S, and walks in the opposite direction around the building once every 40 minutes. If they start at the same time and check the main door each time they pass it, what is the longest interval of time between checks?
After 40 minutes, the second soldier will have gone around the building once, while the first soldier will have gone around twice. This means they will meet at the main door after 40 minutes (LCM of 20 and 40). Therefore, the longest interval of time between checks is 40 minutes.
so what is the answer
The answer is 40 minutes.
why?
The longest interval of time between checks is when the two soldiers first meet at the main door. After 40 minutes, the second soldier will have gone around the building once (since he walks in the opposite direction and takes 40 minutes to complete one round), while the first soldier will have gone around the building twice (since he takes 20 minutes to complete one round). So, they will meet at the main door after 40 minutes, and hence the longest interval between checks is 40 minutes.
can you show me math work for this because i am a visual learner.
Sure, here's the math work:
Let's represent the time in minutes.
First soldier's time to make one round = 20 minutes
Second soldier's time to make one round = 40 minutes
We need to find the LCM of 20 and 40 to determine when they will meet at the main door.
Prime factorizing 20: 20 = 2^2 x 5
Prime factorizing 40: 40 = 2^3 x 5
LCM should contain both 2^2, 2^3 and 5.
LCM = 2^3 x 5 = 40
Therefore, they will meet at the main door after 40 minutes, which means the longest interval of time between checks is 40 minutes.
I hope this helps!