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this is actually really easy...

the one on the inside track has less distance to travel

nice try but not correct. that would be a problem if they were going the same tangential speed but alas they are going the same rotational speed.(think of how it the entire of the second hand on a clock turns at the same time even tough the tip has a longer distance to travel than towards the middle does. the entire second hand has the same rotational speed.)

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The Inner car wins

fossilstoneclocks1rooka.jpg

suppose the inner car is the blue point ,the outer car is the pink one and the finishing line is red

the inner car (the blue point) is clearly reaching the finish line before the outer car(the pink point)

Edited by Rooka
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Clarification: the race track is a perfect circle.

by rotational speed or angular speed, i mean how fast it takes them to move a certain portion of the way around the origin no matter how far or close. So for example, in Rooka's illustration the whole yellow line would reach the finish at the same time

Good thinking Superprasmatic, but the answer is much much simpler.

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we have to say something

if the race distance for the outer car is 10 rounds, so it must be more than 10 rounds for the inner car

coz the distance of one round form outside is much longer than one round from inside....

let`s consider the whole race is one round for the outside car (Red dot).... it is for sure more than one round(may be 2 rounds as in the pic.) for the inner car(Blue dot)

so when they maintain equivalent rotational speeds, they both will make one round at a same time, and here the outer car (red dot) finished the race and wins,while the inner car(blue dot) still needs another round to complete the race....

52094241.jpg

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The finish points are not the same for both cars. The finish point for outer car is slightly behind that for inner car. Since the rotational speeds are the same, the outer car crosses its finish point while the inner car is yet to reach its finish point.

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Does "side by side" mean that the front end of each car crosses the starting line simultaneously?

A silly answer would be that one of the cars travels the wrong way!

congratulations on being the only person who didnt overthink it! you got the right, "silly", answer.

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