$A$ man travelled a distance of $80 \, km$ in $7 \, h$,partly on foot at the rate of $8 \, km/h$ and partly by bicycle at $16 \, km/h$. The distance travelled on foot is (in $km$):

What is the speed of the train in $km/h$?
Statements:
$I.$ The train crosses an $x$ meter-long platform in $n$ seconds.
$II.$ The length of the train is $y$ meters.
$III.$ The train crosses a signal pole in $m$ seconds.

$A$ 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 $300 \text{ m}$ long is running at a speed of $90 \text{ km/h}$. How many seconds will it take to cross a $200 \text{ m}$ long train running in the opposite direction at a speed of $60 \text{ km/h}$?

$P$ and $Q$ are $27 \, km$ apart. Two trains with speeds of $24 \, km/h$ and $18 \, km/h$ respectively start simultaneously from $P$ and $Q$ and travel in the same direction. They meet at a point $R$ beyond $Q$. The distance $QR$ is (in $km$):

$A$ 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 $km/h$):