Select the correct answerIf a person covers the same distance by walking by cycling and by running with speeds in the ratio 1 : 9 : 3 respectively, then the ratio of their times and speeds of the three modes of travel is?Options1 : 81 : 91 : 1 : 181 : 1 : 91 : 9 : 81

The correct answer is 1 : 9 : 81.

Here's the step-by-step explanation:

The speed and time are inversely proportional to each other. This means that if the speed increases, the time taken to cover the same distance decreases and vice versa.

Given the ratio of speeds as 1 : 9 : 3 for walking, cycling, and running respectively, the ratio of time taken will be the inverse of the speed ratio.

So, the ratio of time taken for walking, cycling, and running will be 1/1 : 1/9 : 1/3 = 1 : 1/9 : 1/3.

To make the ratio easier to understand, we can multiply each term by the least common multiple (LCM) of the denominators (9 and 3), which is 9.

So, the ratio of time taken becomes 9 : 1 : 3.

But the question asks for the ratio of time and speed. So, we need to combine the ratios of time and speed.

The ratio of time is 9 : 1 : 3 and the ratio of speed is 1 : 9 : 3.

So, the combined ratio of time and speed is 1 : 9 : 81.

The answer to this question can be found by understanding the relationship between speed, distance, and time. The formula for speed is distance/time. Therefore, the time taken is distance/speed.

Given that the speeds are in the ratio 1:9:3, the times taken will be in the inverse ratio of the speeds. This is because the distance covered is the same in all three cases, so the time taken is inversely proportional to the speed.

So, the ratio of times taken for walking, cycling, and running will be 9:1:3.

The ratio of their speeds is given as 1:9:3.

Therefore, the ratio of their times and speeds of the three modes of travel is 9:1:3:1:9:3.

However, none of the options provided match this answer. There may be a mistake in the question or the options provided.

The correct answer is 1 : 9 : 81.

Here's the step-by-step explanation:

The speed and time of travel are inversely proportional to each other. This means that if the