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

The maximum speed of a train is $80 \mathrm{km}/\mathrm{hr}$. It takes $10$ hours to cover a distance of $400 \mathrm{km}$. The ratio of its maximum speed to its average speed is $2:1$.
Average speed is defined as the ratio of the total distance travelled by a body to the total time taken.

$\mathrm{Average} \mathrm{speed}=\frac{\mathrm{Total} \mathrm{distance}}{\mathrm{Total} \mathrm{time} \mathrm{taken}}$

$\mathrm{Average} \mathrm{speed}=\frac{400 \mathrm{km}}{10\mathrm{ }\mathrm{h}}$

$\mathrm{Average} \mathrm{speed}=40 \mathrm{km}/\mathrm{hr}$

The ratio of maximum speed to its average speed is equal to,

$\frac{\mathrm{Maximum} \mathrm{speed}}{\mathrm{Average} \mathrm{speed}}=\frac{80 \mathrm{km}/\mathrm{hr}}{40 \mathrm{km}/\mathrm{hr} }$

$\frac{\mathrm{Maximum} \mathrm{speed}}{\mathrm{Average} \mathrm{speed}}=\frac{2}{1}$

The ratio of maximum speed to average speed is $2:1$.