02 - Cars moving in opposite directions

Let C = Location where the first car pass 6 minutes before the second
 

 

t₁ = time for the first car to travel from city A to C
$t_1 = \dfrac{x}{50}$
 

t₂ = time for the second car to travel from city B to C
$t_2 = \dfrac{40 - x}{40} = 1 - \dfrac{x}{40}$
 

$t_1 = t_2 + \dfrac{30}{60} - \dfrac{6}{60}$

$\dfrac{x}{50} = \left( 1 - \dfrac{x}{40} \right) + \dfrac{2}{5}$

$\dfrac{9}{200}x = \dfrac{7}{5}$

$x = 31.11 ~ \text{km from city A}$           answer