Question

Two dots move along a circle $1.2$ m long with constant speeds. When they move in different directions, they meet every $15$ seconds. When they move in the same direction, one dot overtakes the other every $60$ seconds. Find the speed of the dots.

Answer 1

let the dots be a and b and their speeds be $x$ and $y$

let us assume a be stationary

$⟹$ for opposite direction speed of $b=x+y$ and for same direction speed of $b=x-y$

$speed=\frac{distance}{time}$

for opp direction $x+y=\frac{1.2}{15}=\frac{2}{25}$

for same direction $x-y=\frac{1.2}{60}=\frac{1}{50}$

on adding both equations we get $x=\frac{1}{20}m/s⟹y=\frac{3}{100}m/s$