A red light flashes 3 times per minute and a green light flashes 5 times in two minutes at regular intervals. If both lights start flashing at the same time, how many times do they flash together in each hour?

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Detailed Solution

Concept- We will first determine the time interval between the red and green lights for one minute in order to answer this question, and then we will move on to consider the common multiple of both the red and green lights in order to arrive at the solution.
Given: A red light flashes three times every minute, while a green light flashes five times every two minutes.
After

\frac{60}{3}

=20 seconds, the red light will flash for the first time in one minute.
That indicates that it will flash every 20 seconds, i.e., 20 sec, 40sec, 60sec, 80sec, 100sec, 120 sec, and so forth (multiples of 20)
Likewise, after

\frac{120}{5}

=24sec, the green light will flash for the first time in two minutes.
That indicates that it will flash every 24 seconds, i.e.,

24 \sec, 48 \sec, 72 \sec, 96 \sec,

120 \sec, 144 \sec

, and so forth (multiples of 24)
Now multiply both the red and green lights by 120 to get their common multiple.
It is also possible by only using the formula