Two trains,each $100 \; m$ long,moving in opposite directions,cross each other in $8 \; s$. If one is moving twice as fast as the other,then the speed (in $km/h$) of the faster train is:

$A$ train $800 \; m$ long is running at a speed of $78 \; km/hr$. If it crosses a tunnel in $1 \; minute$,then the length (in $m$) of the tunnel is:

$A$ train passes a station platform in $36 \; \text{seconds}$ and a man standing on the platform in $20 \; \text{seconds}$. If the speed of the train is $54 \; \text{km/hr}$, what is the length (in $m$) of the platform?

Two trains running at the rate of $45 \; km/h$ and $36 \; km/h$ respectively,on parallel tracks in opposite directions,are observed to pass each other in $8 \; seconds$. When they are running in the same direction at the same rate as before,a person sitting in the faster train observes that he passes the other in $30 \; seconds$. Find the length of the trains (in $m$).

Two stations $P$ and $Q$ are $110 \; km$ apart on a straight line. One train starts from $P$ at $7 \; am$ and travels towards $Q$ at $20 \; km/h$ speed. Another train starts from $Q$ at $8 \; am$ and travels towards $P$ at a speed of $25 \; km/h$. At what time will they meet?

How many seconds will a $500 \;m$ long train take to cross a man walking with a speed of $3 \;km/h$ in the same direction as the moving train,if the speed of the train is $63 \;km/h$?