Two trains start from $P$ and $Q$ respectively and travel towards each other at a speed of $50\, km/hr$ and $40\, km/hr$ respectively. By the time they meet,the first train has travelled $100\, km$ more than the second. The distance between $P$ and $Q$ is (in $km$):

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?

Compare the speed of two trains,one moving at the speed of $80 \, km/h$ and the other at $10 \, m/s$.

$A$ man travels $360 \, km$ in $4 \, hrs$,partly by air and partly by train. If he had travelled all the way by air,he would have saved $\frac{4}{5}$ of the time he was in train and would have arrived at his destination $2 \, hrs$ early. Find the distance he travelled by train (in $km$).

One third of a certain journey is covered at the rate of $25 \, km/hr$,one-fourth at the rate of $30 \, km/hr$,and the rest at $50 \, km/hr$. The average speed for the whole journey is (in $km/hr$):

Two trains,Kanpur Mail and Delhi Mail,start at the same time from stations Kanpur and Delhi respectively towards each other. After passing each other,they take $12\, \text{hours}$ and $3\, \text{hours}$ to reach Delhi and Kanpur respectively. If the Kanpur Mail is moving at the speed of $48\, \text{km/hr}$,the speed of the Delhi Mail is (in $\text{km/hr}$):