$A$ train speeds past a pole in $15 \, \text{seconds}$ and speeds past a $100 \, \text{meters}$ long platform in $25 \, \text{seconds}$. Its length in meters is:

$A$ car during its journey travels $30 \text{ minutes}$ at a speed of $40 \text{ km/h}$,another $45 \text{ minutes}$ at a speed of $60 \text{ km/h}$,and $2 \text{ hours}$ at a speed of $70 \text{ km/h}$. The average speed of the car is (in $\text{km/h}$):

$A$ thief is noticed by a policeman from a distance of $200\, m$. The thief starts running and the policeman chases him. The thief and the policeman run at the speed of $10\, km/h$ and $11\, km/h$ respectively. What is the distance between them after $6\, minutes$? (in $m$)

$A$ 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 $AM$):

$A$ man takes $6\, h \, 15\, min$ in walking a distance and riding back to the starting place. He could walk both ways in $7\, h \, 45\, min$. The time taken by him to ride both ways is:

Walking $\frac{6}{7}$ of his usual speed, a man is $12 \, \text{minutes}$ late. The usual time taken by him to cover that distance is