# Word Problems - Racer

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...

$1200 = (v1 - v2)*200$

$1200 = (v1 + v2)*100$

$v1 - v2 = 6$

$v1 + v2 = 12$

$2v1 = 18$

$v1 = 9$

$v2 = 12 - 9$

$v2 = 3$

Is it right or I made any mistakes ?

• Does "moving in the same sense" mean "moving in the same direction"? – Arturo Magidin Apr 4 '11 at 20:21
• same direction : horizontal; same sense : both right or left; opposite sense: one coming from left, other from right. – user9108 Apr 4 '11 at 20:43
• Looks good to me – Ross Millikan Apr 4 '11 at 22:28

## 1 Answer

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 $v_1 \geq v_2$.

• Isn't it the other way? If I'm running at $v_1=20$ and the other guy is running at $v_2=10$, then my speed relative to the other guy is only 10, not 30. If I'm moving in opposite directions, so I'm approaching him at 20 and he's approaching me at 10, then the relative velocity is 30, because if we started 30 apart we will meet in one time interval. – Arturo Magidin Apr 4 '11 at 20:30
• @Arturo Magidin: of course you are right... I corrected the answer. – Fabian Apr 4 '11 at 20:31