On a tour,a man travels at the rate of $64 \text{ km/h}$ for the first $160 \text{ km}$,then travels the next $160 \text{ km}$ at the rate of $80 \text{ km/h}$. The average speed in $\text{km/h}$ for the first $320 \text{ km}$ of the tour is:

One of the two buses completes a journey of $300 \, km$ in $7 \frac{1}{2} \, hours$ and the other a journey of $450 \, km$ in $9 \, hours.$ The ratio of their average speed is:

$A$ 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:

$A$ man standing on a railway platform observes that a train going in one direction takes $4 \,seconds$ to pass him. Another train of the same length going in the opposite direction takes $5 \,seconds$ to pass him. The time taken (in $seconds$) by the two trains to cross each other will be:

Rakesh sets out to cycle from Delhi to Mathura and at the same time Suresh starts from Mathura to Delhi. After passing each other,they complete their journeys in $9$ and $16 \, \text{hours}$,respectively. At what speed does Suresh cycle if Rakesh cycles at $16 \, \text{km/h}$?

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. What is the time taken by $A$ to reach the destination (in hours)?