Answer:
- 1) 120 seconds
- 2) 180 seconds
Step-by-step explanation:
First light
Shines 3 seconds first time plus after 6 seconds, the pattern is:
Off 6 seconds first time plus after 6 seconds, the pattern is:
Second light
Shines 4 seconds first time plus after 8 seconds, the pattern is:
Off 8 seconds first time plus after 8 seconds, the pattern is:
Third light
Shines 5 seconds first time plus after 10 seconds, the pattern is:
Off 10 seconds first time plus after 10 seconds, the pattern is:
1) All lights will be off after:
- LCM(6x, 8x, 10x) = 2*3*4*5x
- x = 1 ⇒ 120*1 = 120 seconds, next time
2) All lights will come on after:
- LCM(3 + 6x, 4 + 8x, 5 + 10x) = LCM(3(1+2x), 4(1+2x), 5(1 + 2x)) = 60(1 + 2x)
- x = 1 ⇒ 60(1 + 2) = 180 seconds, first time
