$A$ car travels from $P$ to $Q$ at a constant speed. If its speed were increased by $10 \, km/h$,it would have taken $1 \, hour$ less to cover the distance. It would have taken a further $45 \, minutes$ less if the speed was increased by another $10 \, km/h$. The distance between the two cities is (in $km$):

$A$ bus takes $15\, hours$ to travel from Delhi to Chandigarh. The bus travels for one-third of the total time at a speed of $80\, km/h$. It travels for $40\%$ of the remaining time at a speed of $70\, km/h$. It travels for $\frac{2}{3}$ of the remaining time at a speed of $85\, km/h$,and the rest of the time at a speed of $100\, km/h$. What is the total distance covered by the bus?

$A$ train speeds past a pole in $15 \, \text{seconds}$ and speeds past a $100 \, \text{meters}$ long platform in $25 \, \text{seconds}$. Its length in meters is:

$A$ person travels equal distances with speeds of $3 \, km/hr$,$4 \, km/hr$,and $5 \, km/hr$ and takes a total time of $47 \, minutes$. The total distance (in $km$) is:

$A$ dog finds a cat at $25$ leaps away. The cat sees the dog coming towards it and starts running with the dog in hot pursuit. In every minute, the dog makes $5$ leaps and the cat makes $6$ leaps, and one leap of the dog is equal to $2$ leaps of the cat. Find the time in which the dog will catch the cat (in minutes).

$A$ car travels $80 \, km$ in $2 \, hours$ and a train travels $80 \, km$ in $3 \, hours$. The ratio of the speed of the car to that of the train is