$A$ 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 $km$).

Two trains measuring $100\, m$ and $80\, m$ respectively,run on parallel tracks. When travelling in opposite directions,they are observed to pass each other in $9\, s$. When they are running in the same direction at the same speeds as before,the faster train passes the other in $18\, s$. Find the speeds of the two trains in $km/h$.

Heena and Renu are competing in a $100\, m$ race. Initially,Heena runs at twice the speed of Renu for the first $50\, m$. After the $50\, m$ mark,Heena runs at $\frac{1}{4}$ of her initial speed,while Renu continues to run at her original speed. If Renu catches up with Heena at a distance of $N$ meters from the finish line,then $N$ is equal to (in meters).

$A$ car travels a distance of $75 \, km$ at the speed of $25 \, km/h$. It covers the next $25 \, km$ of its journey at the speed of $5 \, km/h$ and the last $50 \, km$ of its journey at the speed of $25 \, km/h$. What is the average speed of the car? (in $km/h$)

$A$ $135\, m$ long train is running with a speed of $54\, km/h$. In what time will it pass a telegraph post? (in $seconds$)

$A$ car driver leaves Bangalore at $8:30 \, am$ and expects to reach a place $300 \, km$ from Bangalore at $12:30 \, pm$. At $10:30 \, am$, he finds that he has covered only $40 \%$ of the distance. By how much does he have to increase the speed of the car in order to keep up with his schedule? (in $km/h$)