There are two racers in a circular racetrack of 1200 meters. When both are moving in the same sense, the first racer comes across the second one every 200 seconds. But in different sense, they come across each other every 100 seconds. What speeds have each one ?
I tried to figure it out but I have no idea how to do it. It's supposed to be a kinematics exercise, since kinematics is mathematics, I asked here. My doubts lay on doing word problems with speed, time and space. I'm so frustrated.
editing... \begin{gather*} \begin{cases}1200 = (v_1 - v_2)\cdot 200\\ 1200 = (v_1 + v_2)\cdot 100 \end{cases}\\ \begin{cases}v_1 - v_2 = 6\\ v_1 + v_2 = 12 \end{cases}\\ 2v_1 = 18\\ v_1 = 9\\ v_2 = 12 - 9 v_2 = 3. \end{gather*}
Is it right or I made any mistakes ?
HINT: Let us denote with $v_1$ ($v_2$) the speed of the first (second) racer. If they are going in opposite directions, the relative speed is the sum $v_1 + v_2$. Going in the same direction, the relative speed is $|v_1 - v_2| = v_1 - v_2$, where we have assumed WLOG that $v_1 \geq v_2$.