Question

every 1/2 hour Naomi stretches her neck; every 1/3 hour she stretches her legs; every 1/6 hour she stretches her arms. what part of her body will Naomi stretch when 2/3 of an hour passes?

Answer 1

She will stretch all the parts of the body that $\frac{2}{3}$ is a  multiple of

She will not strech her neck, $\frac{1}{2}$ multiplied will not give$\frac{2}{3}$

She will however stretch her legs, this will be the second time this hour:
$\frac{1}{3}+\frac{1}{3} =\frac{2}{3}$


She will also stretch her legs, this will be the forth time this hour:
$\frac{1}{6}*4 =\frac{4}{6}=\frac{2}{3}$