Question

Im in need of maijor help this is due soon and i need help ASAP

Answer 1

• 1) 120 seconds
• 2) 180 seconds

Explanation:

First light

Shines 3 seconds first time plus after 6 seconds, the pattern is:

• 3 + 6x

Off 6 seconds first time plus after 6 seconds, the pattern is:

• 6x

Second light

Shines 4 seconds first time plus after 8 seconds, the pattern is:

• 4 + 8x

Off 8 seconds first time plus after 8 seconds, the pattern is:

• 8x

Third light

Shines 5 seconds first time plus after 10 seconds, the pattern is:

• 5 + 10x

Off 10 seconds first time plus after 10 seconds, the pattern is:

• 10x

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