$A$ train running at a speed of $60\, km/h$ crosses a platform double its length in $32.4\, seconds.$ What is the length of the platform? (in $m$)

$A$ man performs $\frac{2}{15}$ of the total journey by rail,$\frac{9}{20}$ by tonga,and the remaining $10 \ km$ on foot. The total journey is (in $km$):

$A$ train,after travelling $50 \, km$,meets with an accident and then proceeds at $\frac{3}{4}$ of its former speed and arrives at its destination $35 \, minutes$ late. Had the accident occurred $72 \, km$ further,it would have reached the destination only $15 \, minutes$ late. The normal speed of the train (in $km/hr$) is:

$A$ train leaves a station $A$ at $7:00 \text{ am}$ and reaches another station $B$ at $11:00 \text{ am}.$ Another train leaves station $B$ at $8:00 \text{ am}$ and reaches $A$ at $11:30 \text{ am}.$ At what time do the two trains cross each other?

$A$ car travels $20\%$ slower than a train. Both start from point $A$ at the same time and reach point $B$ $240\, km$ away at the same time. On the way,the train takes $48\, minutes$ for stopping at stations. What is the speed (in $km/hr$) of the car?

Walking $\frac{6}{7}$ of his usual speed, a man is $12 \, \text{minutes}$ late. The usual time taken by him to cover that distance is