Math CentralQuandaries & Queries


Question from Yukti:

Two people are clapping their hands, but with different frequencies. Ramya claps her hands
17 times per 3 minutes, and Kumar claps his hands 31 times per 5 minutes. They start
clapping at the same time. How many times does each one clap before they clap together at
the same time again?


Suppose that at time $t$ minutes Ramya and Kumar clap together. Ramya claps at the rate of $\large \frac{17}{3}$ claps per minute and hence at time $t$ minutes she claps

\[t \times \frac{17}{3} \mbox{ times.}\]

This is the number of times she claps so it must be an integer. What does that tell you about $t?$


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