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Two taps drip together at exactly 1:00 p.m. One tap then drips again every 68 seconds, while the other tap continues to drip every 72 seconds. At what time will the two taps both drip together again?

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Welcome to Math.SE! You appear to be new here, so I thought I'd give some feedback on your question that you can incorporate in order to receive more (and better!) responses. First: We like to see some of your work. This helps us understand where you're stuck, and enables us to give you a better answer. Second: Copy-paste homework problems aren't well received here. Third: This isn't as important, but still should be mentioned--the homework tag is a "meta" tag. Long story short, this means it shouldn't be the only tag. For example, you could also include algebra-precalculus. –  anorton Feb 6 '13 at 2:56
    
Sorry, I am new here and I understand that you don't want to give answers to homework questions. My daughter is in the 6th grade and has this question. We're at a loss on how to go about finding the answer. We started adding the time up, but I know that is the long and harder way of going about it. I came to realize that every 15 drips, it gains a minute. But then it seems to get out of hand. Any help? –  Perry Feb 6 '13 at 3:01
    
I have a feeling my prior message came across the wrong way... :o. Sorry--I didn't mean to make it sound like you're doing things wrong; I like to give some pointers to people who are new to the site, but I have a feeling I need to change my boiler-plate text... Anyway, Brian M. Scott has given some information, and I gave a hint in my answer as well. If you have more questions about the problem, just leave a comment on one of the answers, and I'm sure we'd both be glad to help. :) –  anorton Feb 6 '13 at 3:06
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4 Answers 4

HINT: If they drip together after $t$ seconds, it must be the case that $t$ is a multiple of both $68$ and $72$. What is the least common multiple of $68$ and $72$?

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Thanks for your help. I appreciate it. –  Perry Feb 6 '13 at 3:09
    
@Perry: You’re welcome. –  Brian M. Scott Feb 6 '13 at 3:11
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Find the smallest $T$ such that $T=68 m = 72n$ for some $m,n >0 $.

$\text{lcm} (68,72) = 1224$ (seconds), so the time at which they are the same again is 1pm+1224 seconds, which is 1:20:24pm

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LCM of 68 and 72=1224 Therefore, time in minutes=1224/60=20 min 4 seconds That's why another drip with the two drops together will be at 1:20:4 pm

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HINT: if they want to drip at the same time, it needs to be:

72*x mod 68 =0.

72 mod 68 = 4

4 * ? =68

if you solve the "?" you need to multiply the value of "?" with 72. Then u got the seconds to the next drip together. transorming to minutes etc should be easy

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