6. Two trains \(A\) and \(B\) leave the same station, \(O\), at 10 a.m. and travel along straight horizontal tracks. \(A\) travels with constant speed \(80 \mathrm {~km} \mathrm {~h} ^ { - 1 }\) due east and \(B\) travels with constant speed \(52 \mathrm {~km} \mathrm {~h} ^ { - 1 }\) in the direction ( \(5 \mathbf { i } + 12 \mathbf { j }\) ) where \(\mathbf { i }\) and \(\mathbf { j }\) are unit vectors due east and due north respectively.

1. Show that the velocity of \(B\) is \(( 20 \mathbf { i } + 48 \mathbf { j } ) \mathrm { km } \mathrm { h } ^ { - 1 }\).
2. Find the displacement vector of \(B\) from \(A\) at 10:15 a.m. Given that the trains are 23 km apart \(t\) minutes after 10 a.m.
3. find the value of \(t\) correct to the nearest whole number.