Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question

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 $72$?

share|cite|improve this answer
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

share|cite|improve this answer

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

share|cite|improve this answer

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

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.