A light bulb garland has two types of bulbs, named A and B. The garland is started exactly at noon and at that instant, both types of bulbs shine together. After that, light bulb A shines after every 15 seconds while light bulb B shines after every 20 seconds (both the bulbs shine for a neglible amount of time). At what time will light bulb A have shone exactly 20 times more than light bulb B?
Question
A light bulb garland has two types of bulbs, named A and B. The garland is started exactly at noon and at that instant, both types of bulbs shine together. After that, light bulb A shines after every 15 seconds while light bulb B shines after every 20 seconds (both the bulbs shine for a neglible amount of time). At what time will light bulb A have shone exactly 20 times more than light bulb B?
Solution
To solve this problem, we need to find a time when bulb A has shone 20 times more than bulb B.
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First, let's determine how often both bulbs shine together. The least common multiple of 15 seconds and 20 seconds is 60 seconds, or 1 minute. This means that every minute, both bulbs shine together.
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Next, let's figure out how many times each bulb shines in one minute. Bulb A shines every 15 seconds, so it shines 4 times in a minute (60/15). Bulb B shines every 20 seconds, so it shines 3 times in a minute (60/20).
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Therefore, in each minute, bulb A shines 1 time more than bulb B (4-3).
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We need bulb A to shine 20 times more than bulb B. Since bulb A shines 1 time more than bulb B per minute, we need 20 minutes for bulb A to shine 20 times more than bulb B (20*1).
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The garland started at exactly noon. Therefore, bulb A will have shone exactly 20 times more than bulb B at 12:20 PM.
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