Arun traveled one-third of the total distance of his trip riding a scooter before it got punctured. He continued the rest of the journey on foot, spending twenty times longer walking than he spent riding. What is the ratio of his riding speed to his walking speed?

Question

Accepted Answer

Let the total distance be $$x$$ kilometers and the total time spent on the trip be $$y$$ hours. Arun covered one-third of the distance riding, which equals $$\frac{x}{3}$$ kilometers. The remaining distance covered by walking is $$x - \frac{x}{3} = \frac{2x}{3}$$ kilometers.

The time spent walking is twenty times longer than the time spent riding. Thus, if the time spent riding is $$y$$, then the time spent walking is $$20y$$.

The speed for riding is calculated as:  
$$
	ext{Riding speed} = \frac{	ext{Distance covered by riding}}{	ext{Time spent riding}} = \frac{\frac{x}{3}}{y} = \frac{x}{3y} \, 	ext{km/hr}.
$$

The speed for walking is calculated as:  
$$
	ext{Walking speed} = \frac{	ext{Distance covered by walking}}{	ext{Time spent walking}} = \frac{\frac{2x}{3}}{20y} = \frac{x}{30y} \, 	ext{km/hr}.
$$

The ratio of riding speed to walking speed is given by:  
$$
	ext{Required ratio} = \frac{	ext{Riding speed}}{	ext{Walking speed}} = \frac{\frac{x}{3y}}{\frac{x}{30y}} = \frac{30}{3} = 10:1.
$$

Thus, the ratio of Arun's riding speed to his walking speed is **10:1**.

Answer

Answer

Answer