the traffic signal at 4th and main turns green every 6 minutes. the signal at 5th and broadway turns green every 4 minutes. if both turned green at 12:15 p. m., when are the next three times that both will turn green at the same time?
every 12 minutes both change at the same time.
Well, it sounds like 4th and Main can be a little green with envy, having to wait 6 whole minutes between greens. Meanwhile, 5th and Broadway gets to strut its stuff every 4 minutes. Life's not fair, huh?
Anyway, let's figure this out. We know that at 12:15 p.m., both signals turned green simultaneously. To find the next three times they'll do the same dance, we need to find a common multiple of 4 and 6.
The least common multiple (LCM) of 4 and 6 is 12. So, the signals will turn green together again after 12 minutes. That gives us the first time, which is 12:27 p.m.
To find the second time, we add another 12 minutes. Now we're at 12:39 p.m.
Finally, let's add another 12 minutes for the third time. Voila! It's 12:51 p.m.
So, the next three times the signals will turn green at the same time are 12:27 p.m., 12:39 p.m., and 12:51 p.m. Enjoy the synchronized traffic light show!
To find the next three times that both traffic signals will turn green at the same time, we need to find the common multiples of 6 minutes and 4 minutes. Let's find the first common multiple after 12:15 p.m.
The first signal at 4th and Main turns green every 6 minutes, so after 12:15 p.m., the signal will turn green at 12:21 p.m., 12:27 p.m., 12:33 p.m., and so on.
The second signal at 5th and Broadway turns green every 4 minutes, so after 12:15 p.m., the signal will turn green at 12:19 p.m., 12:23 p.m., 12:27 p.m., and so on.
To find the common times when both signals turn green, we need to find the common multiples of 6 and 4.
The common multiples of 6 and 4 are: 12, 24, 36, 48, ...
Based on the above information, the next three times that both signals will turn green at the same time are:
1. 12:27 p.m.
2. 12:51 p.m.
3. 1:15 p.m.
To find the next three times that both traffic signals will turn green at the same time, we need to find the least common multiple (LCM) of 6 minutes and 4 minutes.
The LCM is the smallest multiple that both numbers share. In this case, to find the LCM of 6 and 4, we can list their multiples until we find a common multiple:
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, ...
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, ...
From the list, we can see that the least common multiple of 6 and 4 is 12. So, both signals will turn green at the same time every 12 minutes.
Since both signals turned green at 12:15 p.m., we can calculate the next three times they will turn green simultaneously:
1. 12:15 p.m. + 12 minutes = 12:27 p.m.
2. 12:27 p.m. + 12 minutes = 12:39 p.m.
3. 12:39 p.m. + 12 minutes = 12:51 p.m.
Therefore, the next three times that both traffic signals will turn green at the same time are 12:27 p.m., 12:39 p.m., and 12:51 p.m.