$A$ car travelling with $\frac{5}{7}$ of its actual speed covers $42 \, km$ in $1 \, hour \, 40 \, minutes \, 48 \, seconds.$ Find the actual speed of the car (in $km/hr$).

$A$ goods train and a passenger train are running on parallel tracks in the same direction. The driver of the goods train observes that the passenger train coming from behind overtakes and crosses his train completely in $60 \, s$. Whereas a passenger on the passenger train marks that he crossed the goods train in $40 \, s$. If the speeds of the trains are in the ratio of $1:2$,find the ratio of their lengths.

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 $m$):

$A$ 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 $km/hr$)?

Two places $A$ and $B$ are $100 \, km$ apart on a highway. One car starts from $A$ and another from $B$ at the same time. If the cars travel in the same direction at a constant speed,they meet in $5 \, hours$. If the cars travel towards each other,they meet in $1 \, hour$. What is the speed of the car running faster? (in $km/h$)

$A$ bus moving at a speed of $45 \, km/h$ overtakes a truck $150 \, m$ ahead going in the same direction in $30 \, s.$ The speed of the truck is? (in $km/h$)