There are three traffic signals. Each signal changes colour from green to red and then from red to green.…
There are three traffic signals. Each signal changes colour from green to red and then from red to green. The first signal takes 25 seconds, the second signal takes 39 seconds and the third signal takes 60 seconds to change the colour from green to red. The durations for green and red colours are same. At 2:00 p.m., they together turn green. At what time will they change to green next, simultaneously?
4:00 p.m.
4:10 p.m.
4:20 p.m.
4:30 p.m.
Solution
A full green-to-green cycle is twice the green-to-red time: signal cycles are $2 \times 25 = 50$, $2 \times 39 = 78$, $2 \times 60 = 120$ seconds. They turn green together after the LCM of 50, 78 and 120, which is 7800 seconds $= 130$ minutes $= 2$ hours 10 minutes. From 2:00 p.m., the next simultaneous green is at 4:10 p.m.