The Cat and Dog Race Puzzle

The Puzzle:

The Cat and Dog Race
Many years ago, when Barnum's Circus was of a truth "the greatest show on earth" the famous showman got me [Sam Loyd] to prepare for him a series of prize puzzles.

Barnum was particularly pleased with the problem of the cat and dog race.

"A trained cat and dog run a race, 100 feet straightaway and return. The dog leaps three feet at each bound and the cat but two, but then she makes three leaps to his two. Now, under those circumstances, what are the probabilities or possibilities in favor of the one that gets back first?"
Do you have the answer? Check against our solution!