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 travelling with a speed of $60 \, km/h$ catches another train travelling in the same direction and then leaves it $120 \, m$ behind in $18 \, seconds$. The speed of the second train is (in $km/h$):

$A$ man travels $600 \, km$ by train at $80 \, km/hr$, $800 \, km$ by ship at $40 \, km/hr$, $500 \, km$ by aeroplane at $400 \, km/hr$, and $100 \, km$ by car at $50 \, km/hr$. What is the average speed for the entire distance? (in $km/hr$)

$A, B$ and $C$ start at the same time in the same direction to run around a circular stadium. $A$ completes a round in $252 \text{ seconds}$,$B$ in $308 \text{ seconds}$ and $C$ in $198 \text{ seconds}$,all starting at the same point. After what time will they next meet at the starting point again?

The distance between places $A$ and $B$ is $999 \, km$. An express train leaves place $A$ at $6 \, am$ and runs at a speed of $55.5 \, km/h$. The train stops on the way for $1 \, hr \, 20 \, min$. It reaches $B$ at?

The ratio of the speeds of a car,a jeep,and a tractor is $3:5:2$. The speed of the jeep is $250\%$ of the speed of the tractor,which covers $360\,km$ in $12\,hours$. What is the average speed of the car and the jeep together? (in $km/h$)