Question

In a busy city, three roads run parallel to each other. These roads are intersected by a road, running perpendicular to each one of them. At each intersection, traffic signals have been installed. These signals labelled A, B and C change after every 108 seconds, 72 seconds and 48 seconds respectively. These signals are switched on simultaneously at 8.00 a.m.

Based on the above information, answer the following questions.

1. At what time after 8.00 a.m. will all the signals change simultaneously? 
2. At what time after 8.00 a.m. will the signals A and B change simultaneously? 
3. At what time after 8.00 a.m. will the signals B and C change simultaneously?
4. At what time after 8.00 a.m. will the signals A and C change simultaneously?

Answer 1

i. 8:07:12 a.m. 

Working: 108 = 2² × 3³

72 = 2³ × 3²

48 = 2⁴ × 3

LCM = 2⁴ × 3³

= 432 s

= 7 min 12 s

ii. 8:03:36 a.m. 

Working: LCM(108, 72) = 2³ × 3³

= 216 s

= 3 min 36 s

iii. 8:02:24 a.m. 

Working: LCM(72, 48) = 2⁴ × 3²

= 144 s

= 2 min 24 s

iv. 8:07:12 a.m. 

Working: LCM(108, 48) = 2⁴ × 3³

= 432 s

= 7 min 12 s