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 $seconds$)

$A$ 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:

$A$ boy walking at a speed of $10\, km/hr$ reaches his school $15\, minutes$ late. Next time he increases his speed by $2\, km/hr$, but still he is late by $5\, minutes$. Find the distance of his school from his house (in $km$).

$A$ man on tour travels the first $160 \, km$ at $64 \, km/hr$ and the next $160 \, km$ at $80 \, km/hr$. What is the average speed for the first $320 \, km$ of the tour (in $km/hr$)?

Seeta and Geeta cycled towards each other,one from point $A$ and the other from point $B$,respectively. Seeta left point $A$ $6 \, hours$ later than Geeta left point $B$,and it turned out on their meeting that Seeta had travelled $12 \, km$ less than Geeta. After their meeting,they kept cycling with the same speed,and Seeta arrived at $B$ $8 \, hours$ later and Geeta arrived at $A$ $9 \, hours$ later. Find the speed of the faster cyclist in $km/hr$.

$A$ train $700 \, m$ long is running at a speed of $72 \, km/hr$. If it crosses a tunnel in $1 \, minute$,then the length of the tunnel (in $metres$) is: