Ann and Bob are cycling on a track. Ann completes one lap every 15 seconds, and Bob completes one lap every 18 seconds. When will Ann lap Bob, assuming that they started together?
60
Well, let's do some humorous math, shall we? If Ann completes a lap in 15 seconds, and Bob completes a lap in 18 seconds, it means that Ann is faster than Bob. So, Ann is like a speedy hare, and Bob is like a tortoise taking it slow and steady.
Now, we need to find out when Ann will lap Bob. It's like trying to catch a snail with turbo boosters!
To calculate this, we need to find the least common multiple of 15 and 18. Let's see... 15, 30, 45... Hmm, let me check my juggling balls... Ah, got it! The least common multiple is 90 seconds.
Therefore, Ann will lap Bob every 90 seconds. So, Ann might catch up to Bob on their sixth lap, or maybe even earlier if Bob decides to take a leisurely nap on the track.
To find out when Ann will lap Bob, we need to determine the time it takes for Ann to complete one extra lap compared to Bob. Let's call this time "T".
To calculate "T", we can find the least common multiple (LCM) of the two lap times. The LCM of 15 seconds and 18 seconds will give us the time it takes for both Ann and Bob to complete a whole number of laps simultaneously.
To find the LCM of 15 and 18, we can list the multiples of both numbers until we find the first common multiple:
Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, ...
Multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144, ...
We can see that 90 is the first common multiple of both 15 and 18. This means that Ann and Bob will meet and complete a whole number of laps together after 90 seconds.
Now, we need to determine how many laps Ann will complete in those 90 seconds. Since Ann completes one lap every 15 seconds, we divide the total time (90 seconds) by 15:
90 seconds ÷ 15 seconds/lap = 6 laps
Therefore, Ann will lap Bob after 6 laps.
To find out at what time this occurs, we multiply the lap time (18 seconds) by the number of laps (6):
18 seconds/lap × 6 laps = 108 seconds
Therefore, Ann will lap Bob after 108 seconds.
To convert this to a more readable format, we can express it as 1 minute and 48 seconds. Hence, Ann will lap Bob after 1 minute and 48 seconds.