In a $1 \, km$ race,$A, B$,and $C$ are three participants. $A$ can give $B$ a start of $50 \, m$ and $C$ a start of $69 \, m$. The start,which $B$ can allow $C$ is (in $m$):

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 $200 \, m$ 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?

$A$ 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.

$A$ train $800 \, m$ long is running at a speed of $78 \, km/h$. If it crosses a tunnel in $1 \, minute$,then the length of the tunnel (in $m$) is:

$A$ car covers four successive $3 \, km$ stretches at speeds of $10 \, km/h$,$20 \, km/h$,$30 \, km/h$,and $60 \, km/h$ respectively. Its average speed over this total distance is (in $km/h$):