$A$ train leaves station $A$ at $5\, AM$ and reaches station $B$ at $9\, AM$ on the same day. Another train leaves station $B$ at $7\, AM$ and reaches station $A$ at $10.30\, AM$ on the same day. The time at which the two trains cross one another is (in $AM$):

$A$ train passes through a telegraph post in $9$ $seconds$ moving at a speed of $54 \, km/h$. The length of the train is (in $meters$):

$A$ car travels a distance of $75 \, km$ at the speed of $25 \, km/h$. It covers the next $25 \, km$ of its journey at the speed of $5 \, km/h$ and the last $50 \, km$ of its journey at the speed of $25 \, km/h$. What is the average speed of the car? (in $km/h$)

Walking at three-fourth of his usual speed, a man covers a certain distance in $2 \, \text{hours}$ more than the time he takes to cover the distance at his usual speed. The time taken by him to cover the distance with his usual speed is (in $\text{hours}$):

$A$ goods train and a passenger train are running on parallel tracks in the same direction. The driver of the goods train observes that the passenger train coming from behind overtakes and crosses his train completely in $60 \, s$. Whereas a passenger on the passenger train marks that he crossed the goods train in $40 \, s$. If the speeds of the trains are in the ratio of $1:2$,find the ratio of their lengths.

$A$ train,$300 \, m$ long,passes a man walking along the line in the same direction at the rate of $3 \, km/h$ in $33 \, s$. The speed of the train is (in $km/h$):