Two men are running on a circular track. They start from the same position. If they take 3 minutes and 5 minutes to run once around the track, find the time interval between successive crossings and the number of times they cross each other in an hour if they travel the path in (i) opposite sense (ii) same sense

PLACEHOLDER ANSWER - the question has four answers. Their rates are $$\frac{1}{3}$$ and $$\frac{1}{5}$$ of a lap per minute. (i) In opposite senses they close a full lap at $$\frac{1}{3} + \frac{1}{5} = \frac{8}{15}$$ lap per minute, so they cross every $$\frac{15}{8} = 1.875$$ minutes, 32 times in an hour. (ii) In the same sense they close at $$\frac{1}{3} - \frac{1}{5} = \frac{2}{15}$$ lap per minute, so they cross every 7.5 minutes, 8 times in an hour.