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 covers a certain distance between his house and office on a scooter. With an average speed of $30 \, km/hr$,he is late by $10 \, min$. However,with a speed of $40 \, km/hr$,he reaches his office $5 \, min$ earlier. Find the distance between his house and office in $km$.

$A$ 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 $km/h$.

$A$ car covers the first $39 \, km$ of its journey in $45 \, minutes$ and the remaining $25 \, km$ in $35 \, minutes$. What is the average speed of the car in $km/h$?

$A$ $180\, m$ long train crosses another $270\, m$ long train running in the opposite direction in $10.8\, seconds$. If the speed of the first train is $60\, km/h$, what is the speed of the second train in $km/h$?

Two trains of equal length take $10 \, s$ and $15 \, s$ respectively to cross a telegraph post. If the length of each train is $120 \, m$,in what time (in $s$) will they cross each other while travelling in the same direction?