$A$ man can reach a certain place in $30 \, \text{hours}$. If he reduces his speed by $\frac{1}{15}^{th}$, he goes $10 \, \text{km}$ less in that same time. Find his speed in $\text{km/hr}$.

$A$ student walks from his house at a speed of $2 \, km/h$ and reaches his school $6 \, minutes$ late. The next day,he increases his speed by $1 \, km/h$ and reaches $6 \, minutes$ before school time. How far is the school from his house? (in $km$)

Two trains measuring $100\, m$ and $80\, m$ respectively,run on parallel tracks. When travelling in opposite directions,they are observed to pass each other in $9\, s$. When they are running in the same direction at the same speeds as before,the faster train passes the other in $18\, s$. Find the speeds of the two trains in $km/h$.

Two men are standing on opposite ends of a bridge of $1200 \, m$ long. If they walk towards each other at the rate of $5 \, m/min$ and $10 \, m/min$ respectively,in how much time will they meet each other? (in $minutes$)

$A$ man walks from $A$ to $B$ and back in a certain time at the rate of $3.5 \text{ km/h}$. If he had walked from $A$ to $B$ at the rate of $3 \text{ km/h}$ and back from $B$ to $A$ at the rate of $4 \text{ km/h}$,he would have taken $5 \text{ minutes}$ longer. Find the distance between $A$ and $B$ (in $\text{km}$).

Amit starts his journey from Patna to Delhi at a speed of $50 \, km/h$. The distance between Delhi and Patna is $1000 \, km$. He takes a rest of $20 \, minutes$ after every $3 \, hours$ of driving. How much total time will he take to reach Delhi? (in $hrs$)