It takes $24 \, s$ for a train travelling at $93 \, km/h$ to cross entirely another train half its length travelling in the opposite direction at $51 \, km/h$. It passes a bridge in $66 \, s$. What is the length of the bridge in meters?

$A$ train starts from station $A$ at $9\, am$ and travels at $50\, km/h$ towards station $B,$ which is $210\, km$ away. Another train starts from station $B$ at $11\, am$ and travels at $60\, km/h$ towards station $A.$ At what distance from station $A$ will they meet? (in $km$)

Two trains $M$ and $N$ cross a pole in $25 \text{ seconds}$ and $1 \text{ minute } 15 \text{ seconds}$ respectively. The length of train $M$ is half the length of train $N$. What is the respective ratio between the speed of train $M$ and train $N$?

$A$ train goes from Ballygunge to Sealdah at an average speed of $20 \text{ km/h}$ and comes back at an average speed of $30 \text{ km/h}$. The average speed of the train for the whole journey is (in $\text{km/h}$)

$A$ car starts from $A$ for $B$ travelling at $20 \, km/h$. $1 \frac{1}{2} \, hours$ later,another car starts from $A$ and,travelling at the rate of $30 \, km/h$,reaches $B$ $2 \frac{1}{2} \, hours$ before the first car. Find the distance from $A$ to $B$ (in $km$).

$A$ person covers half of his journey at $30 \text{ km/h}$ and the remaining half at $20 \text{ km/h}$. The average speed for the whole journey is (in $\text{km/h}$)