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)?

$A$ motorcyclist left $6 \frac{2}{3}$ minutes later than the scheduled time,but in order to reach his destination $21 \, km$ away on time,he had to increase his speed by $12 \, km/h$ from his usual speed. What is the usual speed (in $km/h$) of the motorcyclist?

$A$ train $200 \, m$ long is running at a speed of $20 \, m/s$. In how much time (in $seconds$) will it cross a bridge of $400 \, m$ length?

Anna left for city $A$ from city $B$ at $5:20\, a.m.$ She travelled at a speed of $80\, km/h$ for $2\, hours\, 15\, minutes.$ After that,the speed was reduced to $60\, km/h.$ If the total distance between the two cities is $350\, km,$ at what time did Anna reach city $A$?

Raj and Prem walk in opposite directions at the rate of $3 \, km/h$ and $2 \, km/h$ respectively. How far will they be from each other after $2 \, hours$? (in $km$)

Two trains are running at a speed of $40 \, km/h$ and $20 \, km/h$ respectively in the same direction. The fast train completely passes a man sitting in the slow train in $5 \, seconds$. The length of the fast train is (in $m$):