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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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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

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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