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 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?

Hi,

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 $t?$

Penny

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