Let's assume the speeds of the three cars are 3x, 4x, and 5x, respectively, where x is a common factor.
The time taken to travel a certain distance is inversely proportional to the speed. This means that the ratio of the time taken by the cars will be the reciprocal of their speed ratios.
So, the ratios of the time taken by the three cars would be:
1/(3x) : 1/(4x) : 1/(5x)
Simplifying the ratios:
1/(3x) = 1/3x 1/(4x) = 1/4x 1/(5x) = 1/5x
The simplified ratios are:
1:3/4:1/5
To make the ratios more convenient, we can multiply each ratio by a factor that would result in whole numbers. In this case, we can multiply each ratio by 20:
20:15:4
Therefore, the ratios of the time taken by the three cars to travel the same distance are 20:15:4.