By walking at $\frac{3}{4}$ of his usual speed,a man reaches his office $20 \text{ minutes}$ later than usual. His usual time is (in $\text{minutes}$):

$A$ $280 \, m$ long train moving with an average speed of $108 \, km/h$ crosses a platform in $12 \, s$. $A$ man crosses the same platform in $10 \, s$. What is the speed of the man in $m/s$?

$A$ 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 $m$)

If a train runs at $40 \text{ km/h}$,it reaches its destination late by $11 \text{ minutes}$. But if it runs at $50 \text{ km/h}$,it is late by $5 \text{ minutes}$ only. The correct time (in $\text{minutes}$) for the train to complete the journey is

Two places $P$ and $Q$ are $162 \, km$ apart. $A$ train leaves $P$ for $Q$ and simultaneously another train leaves $Q$ for $P$. They meet at the end of $6 \, hours$. If the former train travels $8 \, km/h$ faster than the other,then the speed of the train from $Q$ is (in $km/h$):

$A$ and $B$ run a kilometer and $A$ wins by $25 \, s.$ $A$ and $C$ run a kilometer and $A$ wins by $275 \, m.$ When $B$ and $C$ run the same distance,$B$ wins by $30 \, s.$ The time taken by $A$ to run a kilometer is?