Amit started cycling along the boundaries of a square field from corner point $A$. After half an hour,he reached the corner point $C$,diagonally opposite to $A$. If his speed was $8 \, km/h$,what is the area of the field in square $km$?

$A, B$ and $C$ start together from the same place to walk around a circular path of length $12 \, km$. $A$ walks at the rate of $4 \, km/h$,$B$ at $3 \, km/h$,and $C$ at $\frac{3}{2} \, km/h$. They will meet together at the starting place at the end of (in $h$):

Two trains,one $160 \, m$ and the other $140 \, m$ long,are running in opposite directions on parallel tracks. The first is moving at $77 \, km/h$ and the other at $67 \, km/h$. How long will they take to cross each other? (in $seconds$)

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.

The average speed of a train is $1 \frac{3}{7}$ times the average speed of a car. The car covers a distance of $588 \text{ km}$ in $6 \text{ hours}$. How much distance will the train cover in $13 \text{ hours}$? (in $\text{km}$)

By walking at $\frac{3}{4}$ of his usual speed,a man reaches his office $20 \text{ minutes}$ later than usual. His usual time is (in $\text{minutes}$):