$A$ man driving at $\frac{3}{4}$ of his original speed reaches his destination $20 \text{ minutes}$ later than the usual time. Then the usual time is (in $\text{minutes}$)

$A$ walks around a circular field at the rate of one $round/hour$,while $B$ runs around it at the rate of six $rounds/hour$. They start in the same direction from the same point at $7.30 \, a.m$. They shall first cross each other at (in $a.m.$)

$A$ hare sees a dog $100\, m$ away from her and runs off in the opposite direction at a speed of $12\, km/h$. $A$ minute later,the dog perceives her and gives chase at a speed of $16\, km/h$. How much distance is covered by the hare after being spotted? (in $m$)

In covering a certain distance,the speeds of $A$ and $B$ are in the ratio of $3:4$. $A$ takes $30 \text{ minutes}$ more than $B$ to reach the destination. The time taken by $A$ to reach the destination is (in $\text{hours}$):

An express train travelled at an average speed of $100 \, km/hr$, stopping for $3 \, minutes$ after every $75 \, km$. How long did it take to reach its destination $600 \, km$ from the starting point?

The speed of a car increases by $2\, km/h$ after every hour. If the distance travelled in the first hour was $35\, km$,what is the total distance travelled in $12$ hours? (in $km$)