$A$ train travelling at a speed of $55\, km/hr$ travels from place $X$ to place $Y$ in $4\, hours$. If its speed is increased by $5\, km/hr$,then the time of journey is reduced by (in $minutes$):

$A$ car starts from $A$ for $B$ travelling at $20 \, km/h$. $1 \frac{1}{2} \, hours$ later,another car starts from $A$ and,travelling at the rate of $30 \, km/h$,reaches $B$ $2 \frac{1}{2} \, hours$ before the first car. Find the distance from $A$ to $B$ (in $km$).

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. Find the correct time for the train to complete its journey (in minutes).

$A$ man walks $6 \, km$ at a speed of $1 \frac{1}{2} \, km/h$,runs $8 \, km$ at a speed of $2 \, km/h$,and travels another $32 \, km$ by bus. The speed of the bus is $8 \, km/h$. Find the average speed of the man in $km/h$.

Two men $A$ and $B$ walk from $P$ to $Q$ at a distance of $21 \text{ km}$ at speeds of $3 \text{ km/h}$ and $4 \text{ km/h}$ respectively. $B$ reaches $Q$ and returns immediately and meets $A$ at $R$. The distance from $P$ to $R$ is (in $\text{km}$):

$A$ man takes $6$ hours $30$ minutes in walking to a certain place and riding back. He would have gained $2$ hours $10$ minutes by riding both ways. How long would he take to walk both ways? (in minutes)