The two car (say A and B) are moving with same velocity, the relative velocity of one (say B) with respect to the other A, \vec{v}_{BA} = \vec{v}_B - \vec{v}_A = \vec{v} - \vec{v} = 0

So the relative separation between them (= 5 km) always remains the same.

Now if the velocity of car (say C) moving in opposite direction to A and B, is \vec{v}_{c} relative to ground then the velocity of car C relative to A and B will be \vec{v}_{rel} = \vec{v}_c - \vec{v}

But as \vec{v} is opposite to v _C

So \(\mathbf{v}_{rel} = \mathbf{v}_c - (-30) = (\mathbf{v}_c + 30) \text{ km/hr}.\)

So, the time taken by it to cross the cars A and B \(t = \frac{d}{v_{\mathrm{rel}}} \Rightarrow \frac{4}{60} = \frac{5}{v_c + 30}\)

\(\Rightarrow v_{c} = 45 \text{ km/hr.}\)