$A$ thief is stopped by a policeman from a distance of $150\, m$. When the policeman starts the chase,the thief also starts running. Assuming the speed of the thief as $7\, km/h$ and that of the policeman as $9\, km/h$,how far would the thief have run before he is overtaken by the policeman? (in $m$)

$A$ $300 \, m$ long train is travelling with a speed of $45 \, km/hr$ when it passes point $A$ completely. At the same time,a motorbike starts from point $A$ with a speed of $70 \, km/hr$. When it exactly reaches the middle point of the train,the train increases its speed to $60 \, km/hr$ and the motorbike reduces its speed to $65 \, km/hr$. How much distance will the motorbike travel while passing the train completely? (in $km$)

$A$ 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.

$A$ man with $\frac{3}{5}$ of his usual speed reaches the destination $2 \frac{1}{2}$ hours late. Find his usual time to reach the destination? (in $hours$)

Train $A$ starts its journey from Patna to Hazipur while train $B$ starts from Hazipur to Patna. After crossing each other, they finish their journey in $81\, \text{hours}$ and $121\, \text{hours}$ respectively. What will be the speed of train $B$ if the speed of train $A$ is $44\, \text{km/h}$?

$A$ train covers a distance between station $A$ and station $B$ in $45 \, min$. If the speed of the train is reduced by $5 \, km/h$,then the same distance is covered in $48 \, min$. The distance between stations $A$ and $B$ is? (in $km$)