I27-25

Question

On July 4th, a town holds an annual fireworks show. The show’s finale features two types of fireworks—Firework A and Firework B—launched at regular intervals to create a synchronized effect in the sky.
 
• Firework A is launched every 6 seconds.
 
• Firework B is launched every 21 seconds.
 
They are first launched together at the exact start of the finale, and the time required to launch a firework is negligible.
 
Based on the above information, select for  Time  the number of seconds after the start of the finale both Firework A and Firework B next launch simultaneously and select for  Launches  the number of times Firework A will have been launched before that moment.

Bunuel · Answer

Official Solution:

Firework A launches every 6 seconds: 0, 6, 12, 18, 24, 30, 36, 42, ...
 
Firework B launches every 21 seconds: 0, 21, 42, ...
 
The first time both launch together again after time 0 is at 42 seconds.
 
By then, Firework A has launched at: 0, 6, 12, 18, 24, 30, 36 — 7 times before 42.

Correct answer:

Time  "42"

Launches  "7"

sindhureddyalla · Answer

Why do we have to consider 0 ?

Bunuel · Answer

We consider 0 because the question says they are first launched together at the exact start of the finale.

That initial launch at 0 seconds counts as the first launch for both fireworks. So when we count how many times Firework A has been launched by 42 seconds, we must include the launch at 0.

isteducimus · Answer

I did this by taking LCM of 6 and 21. is the approach correct? 
3rd time these would be together would be LCM*2 and so on?

Bunuel · Answer

Yes, your LCM approach is correct. LCM(6, 21) = 42, so the first common launch after time 0 is at 42 seconds. After that, they’ll meet again at multiples of 42 (84, 126, ...).

anshumannanda · Answer

I like the solution - it’s helpful.

I27-25

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