Two men start together to walk a certain distance,one at $4 \, km/h$ and another at $3 \, km/h$. The former arrives half an hour before the latter. Find out the distance in $km$.

$A$ 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 $km$).

$A$ train runs at an average speed of $75\, km/hr$. If the distance to be covered is $1050\, km$, how long will the train take to cover it? (in $hrs$)

$A$ train passes a $150 \,m$ long railway bridge in $18 \,seconds$. If the train is running at a speed of $60 \,km/h$,then the length of the train in metres is (in $m$).

Buses start from a bus terminal with a speed of $20 \text{ km/h}$ at intervals of $10 \text{ mins}$. What is the speed of a man coming from the opposite direction towards the bus terminal if he meets the buses at intervals of $8 \text{ mins}$? (in $\text{km/h}$)

The speed of a car increases by $2\, km/h$ after every hour. If the distance travelled in the first hour was $35\, km$,what is the total distance travelled in $12$ hours? (in $km$)