The maximum speed of a train is $80\mathit{ km}/\mathit{hr}$. It takes $10$ hours to cover a distance of $400\mathit{ km}$. the ratio of its maximum speed to its average speed is __________.

Solution:

The maximum speed of a train is $80\mathit{ km}/\mathit{hr}$. It takes $10$ hours to cover a distance of $400\mathit{ km}$. the ratio of its maximum speed to its average speed is $2:1$.
Average speed is defined as the ratio of total distance travelled by a body to total time taken.
$\mathit{Average\; speed}=\frac{\mathit{Total\; distance}}{\mathit{Total\; time\; taken}}$
$\mathit{Average\; speed}=\frac{400\mathit{ km}}{10 h}$
$\mathit{Average\; speed}=40\mathit{ km}/\mathit{hr}$
The ratio of maximum speed to its average speed is equal to,
$\frac{\mathit{Maximum\; speed}}{\mathit{Average\; speed}}=\frac{80\mathit{ km}/\mathit{hr}}{40\mathit{ km}/\mathit{hr }}$
$\frac{\mathit{Maximum\; speed}}{\mathit{Average\; speed}}=\frac{2}{1}$
The ratio of maximum speed to average speed is $2:1$.