Two men start together to walk a certain distance,one at $4 \, km/h$ and another at $3 \, km/h$. The former arrives half an hour before the latter. Find out the distance in $km$.

In covering a certain distance,the speeds of $A$ and $B$ are in the ratio of $3:4$. $A$ takes $30 \text{ minutes}$ more than $B$ to reach the destination. The time taken by $A$ to reach the destination is (in $\text{hours}$):

$A$ 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 $km$):

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 $km/hr$.

What is the length of the bridge (in $m$) that a man riding at $15 \, km/h$ can cross in $5 \, minutes$?

$A$ 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: