#### Answer

It will take 4.2 minutes for the two cars to meet.

#### Work Step by Step

Let north be the positive direction.
Let $v_{B,r}$ be the velocity of the BMW relative to the road.
$v_{B,r} = 100.0~km/h$
Let $v_{V,r}$ be the velocity of the VW relative to the road.
$v_{V,r} = -42.0~km/h$
We can find $v_{B,V}$, the velocity of the BMW relative to the VW:
$v_{B,r} = v_{B,V}+v_{V,r}$
$v_{B,V} = v_{B,r}-v_{V,r}$
$v_{B,V} = 100.0~km/h-(-42.0~km/h)$
$v_{B,V} = 142.0~km/h$
The velocity of the BMW relative to the VW is $142.0~km/h$ north
We can find the time it takes the BMW to meet the VW:
$t = \frac{d}{v} = \frac{10.0~km}{142.0~km/h} = 0.07~h = 4.2~min$
It will take 4.2 minutes for the two cars to meet.