[Prof. Templeton]

Many years ago, back when Professor Templeton was a young lad, he witnessed a foot race between two people. A nurse and a firefighter had got together on the first of April to run a race with each other and for the benefit of those in attendance. The race was to be 100 feet straight to a turning point and 100 feet back to the starting point. It was found that the firefighter ran 3 feet at every step and the nurse only 2, but then she made 3 steps to his 2 steps. There was no catch in the distance of the race, meaning its total was indeed 200 feet for both runners, and the amount of time spent at the turn was the same for each, but the race did not end in a tie. What was the result of the race?

[Prof. Templeton]

I thought I should re-read the OP and see if I could have made any other false assumptions. When trying to determine whether the firefighter or the nurse are faster, I assumed the nurse was a female (she) and the firefighter a male (he). Based on that, I assumed that they both ran at pretty much the same speed. But if the female was in fact the firefighter and the man the nurse, then the firefighter is clearly the faster (3 steps of 3 feet for every 2 steps of 2 feet). So I think that it is possible that the race was run by a female firefighter and a male nurse and the firefighter easily won the race.

Ding Ding Ding! Give that dude a prize!

[Prof. Templeton]

The firefighter won. And quite handily too. She won by 111 feet and 1-1/3 inches. Yes the firefighter was the female and her steps were 3 feet to the male nurse's 2 feet and she also took 3 steps to his 2. Thus, she covered 9 feet in the time it took our out-of-shape male nurse to go 4 feet. Since there was no tie, every step taken was either 3 feet or 2 feet respectively and the distance was 200 feet exactly, the only possible solution is that the firefighter was the "she" that was referred too. Also since I stated that it was a race that "I had witnessed" it was a particular firefighter and nurse and not a general case. Back in the late 1800's when a version of this puzzle was put forth, the solution was never correctly submitted and the author had to eventually let the cat out of the bag. I guess we've come a long way.

[Guest]

The firefighter won. And quite handily too. She won by 111 feet and 1-1/3 inches. Yes the firefighter was the female and her steps were 3 feet to the male nurse's 2 feet and she also took 3 steps to his 2. Thus, she covered 9 feet in the time it took our out-of-shape male nurse to go 4 feet. Since there was no tie, every step taken was either 3 feet or 2 feet respectively and the distance was 200 feet exactly, the only possible solution is that the firefighter was the "she" that was referred too. Also since I stated that it was a race that "I had witnessed" it was a particular firefighter and nurse and not a general case. Back in the late 1800's when a version of this puzzle was put forth, the solution was never correctly submitted and the author had to eventually let the cat out of the bag. I guess we've come a long way.

You're kidding... That twist popped into my head immediately but was discounted just as quickly. Had I carefully re-read the OP... Well played Prof. Especially the date of the race.

[Guest]

The nurse wins the race. She needs exactly 100 steps to complete the 200 foot race. The firefighter must take 68 steps in order to travel a total distance of 204 feet, which would be required in order to cross the checkpoint and finish line. The nurse takes 3 steps to his two, so she can take 100 steps to his 66 2/3 steps. Therefore he is a step behind her as she crosses the finish line.