Ex 3.7, 6 (Introduction) The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they change simultaneously at 7 a.m., at what time will they change simultaneously again?Let the traffic lights change in 1 second, 2 second, 3 seconds
At 6 seconds, all of them change again.
Now, this 6 is actually the LCM of 1, 2, 3
So, Time when they change again = LCM of 1, 2, 3
Ex 3.7, 6 The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they change simultaneously at 7 a.m., at what time will they change simultaneously again?Traffic Lights change every 48 seconds, 72 seconds, 108 seconds
We need to find
the time when they change simultaneously
Now, time when they change again will be more than 48, 72, 108
So we find LCM
Time when they change again = LCM of 48, 72, 108
LCM of 48, 72, 108
LCM = 2 2 2 2 3 3 3
= 16 27
= 432
Time when they change again = 432 seconds
But
We need to find time after 7 am
So, first we convert 432 seconds into minutes
Time = 432 seconds = 432/60 minutes
Time = 7 Minutes 12 Seconds
Thus
Required Time = 7am + 7 minutes 12 Seconds
= 7:07:12 am

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.