Two trains $A$ and $B$ travel on two parallel rail tracks in opposite directions with speeds $v_1$ and $v_2$,respectively. They take $4 \ s$ to pass each other at these speeds. If the speed of train $A$ is increased by $50 \%$,then they take $3 \ s$ to pass each other. The ratio $v_1 / v_2$ is:

Two cars,at a certain instant,are $50 \ km$ apart on a line running from south to north. The one farther north is moving west at $25 \ km/hr$. The other is moving towards north at $25 \ km/hr$. How long do they take to reach their distance of closest approach (in $min$)?

For the two given particles $A$ and $B$ as shown in the figure,how much time will it take for their horizontal separation to become zero?

$A$ train of $150 \; m$ length is going towards the north direction at a speed of $10 \; m/s$. $A$ parrot flies at a speed of $5 \; m/s$ towards the south direction parallel to the railway track. The time taken by the parrot to cross the train is: (in $; s$)

Car $A$ is moving to the East with a speed of $30 \text{ km/h}$,and car $B$ is moving to the North with the same speed. What is the velocity of car $B$ as measured from car $A$?

Ship $A$ is sailing towards north-east with velocity $\vec{v}_A = 30\hat{i} + 50\hat{j}\,\text{km/hr}$,where $\hat{i}$ points east and $\hat{j}$ points north. Ship $B$ is at a distance of $80\,\text{km}$ east and $150\,\text{km}$ north of Ship $A$ and is sailing towards west at $10\,\text{km/hr}$. After how many hours will Ship $A$ be at the minimum distance from Ship $B$?