If the length of the train is $700 \, m$ and the length of the platform is $500 \, m$,find the time taken by the train moving at $54 \, km/h$ to cross the platform (in $sec$).

$A$ train covers a distance between station $A$ and station $B$ in $45\, minutes.$ If the speed of the train is reduced by $5\, km/h,$ then the same distance is covered in $48\, minutes.$ The distance between stations $A$ and $B$ is (in $km$):

Sound travels $330 \text{ m/s}$. If the sound of a thundercloud is heard $10 \text{ s}$ after the flash,the distance of the thundercloud is (in $\text{km}$):

$A$ man starts from a place $P$ and reaches the place $Q$ in $7 \, hours$. He travels $\frac{1}{4}^{th}$ of the distance at $10 \, km/h$ and the remaining distance at $12 \, km/h$. The distance,in $km$,between $P$ and $Q$ is

One aeroplane started $30 \, \text{minutes}$ later than the scheduled time from a place $1500 \, \text{km}$ away from its destination. To reach the destination at the scheduled time,the pilot had to increase the speed by $250 \, \text{km/hr}$. What was the original speed of the aeroplane? (in $\text{km/hr}$)

Two places $A$ and $B$ are $100 \, km$ apart on a highway. One car starts from $A$ and another from $B$ at the same time. If the cars travel in the same direction at a constant speed,they meet in $5 \, hours$. If the cars travel towards each other,they meet in $1 \, hour$. What is the speed of the car running faster? (in $km/h$)