Question

Three women, Chantel, Marissa, and Qian, enjoy running laps around a circular track. Each women runs at a constant speed. It takes Qian 150 seconds to run around the track. Marissa, who is running in the opposite direction as Qian, meets Qian every 60 seconds. Chantel, who is running in the same direction as Marissa, passes Marissa every 300 seconds. How often does Chantel meet Qian?

Answer 1

It takes 150 seconds for Qian to complete the track.

Let she runs the track in the clockwise direction.

In 60 seconds, she runs $\frac{60}{150}$ = $\frac{2}{5}$th of the track.

Since she meets Marissa, who is running in the opposite (counter clockwise) direction in every 60 seconds, Marissa should have completed $\frac{3}{5}$th of the track.

Chantel meets Marissa in every 300 seconds.

So, in 60 seconds, she advances Marissa by $\frac{1}{5}$th of the track.

Hence, in 300 seconds, Qian, Marissa and Chantel all meets at the starting point.

ALITER;

Marissa meets Qian in every 60 seconds.

So, Marissa and Qian meet each other in 60th, 120th, 180th, 240th and 300th second.

But, it is given that Chantel meets Marissa in every 300 seconds.

So, in 300 seconds, Qian, Marissa and Chantel meet each other.