# 05 - Two runners moving in opposite directions in a circular track

**Problem**

Benjie and Jerwin is running in opposite directions in a 400-meter circular track and meet each other every 35 seconds. If Benjie can complete one track in 65 seconds. How long does it take for Jerwin to run 400 meters?

**Solution**

Rate of Benjie

$v_B = \dfrac{400}{65} = \dfrac{80}{13}$

$v_B = \dfrac{400}{65} = \dfrac{80}{13}$

Rate of Jerwin

$v_J = \dfrac{400}{t}$

Benjie and Jerwin run a total of 400 m in 35 seconds

$s_B + s_J = 400$

$\left( \dfrac{80}{13} \right)(35) + \left( \dfrac{400}{t} \right)(35) = 400$

$\dfrac{7}{13} + \dfrac{35}{t} = 1$

$\dfrac{35}{t} = \dfrac{6}{13}$

$t = 75.83 ~ \text{sec}$ *answer*

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