[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?

[Pickett]

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?

I'm working right now, and don't have much time to get into thinking everything through...however, at first thought, since the nurse runs 2 feet every step, she will evenly hit the 100 foot mark...but the firefighter will have 1 foot left where he would probably have to do a stutter step or something to hit that point...OR if he just kept running at his normal pace, he would have hit the 102 foot mark before being allowed to turn around, in which case, the nurse would win, because she traveled less distance.

[HoustonHokie]

For each leg of the race, the firefighter has to take 100/3 = 33.33 => 34 steps, or 68 steps total.

For each leg of the race, the nurse has to take 100/2 = 50 steps, or 100 steps total.

She takes 3 steps for every 2 of his, so, because 100/68 < 3/2, the nurse wins.

[Pickett]

For each leg of the race, the firefighter has to take 100/3 = 33.33 => 34 steps, or 68 steps total.

For each leg of the race, the nurse has to take 100/2 = 50 steps, or 100 steps total.

She takes 3 steps for every 2 of his, so, because 100/68 < 3/2, the nurse wins.

that's what I was saying in my first post, but this is just a better explanation :c)

[Guest]

I was thinking that since the FF has to take 66.666 steps to cover the 200' race and the nurse has to take 100 steps, that the nurse's foot stops exactly at the 200' mark while the FF's foot travels through the finish line. I see it as the FF wins

[Pickett]

I was thinking that since the FF has to take 66.666 steps to cover the 200' race and the nurse has to take 100 steps, that the nurse's foot stops exactly at the 200' mark while the FF's foot travels through the finish line. I see it as the FF wins

But, the firefighter can't turn around at the halfway point until he has PASSED the 100' line...he won't do that until he has taken 33.33333 steps...which means he needs to take 34 steps before he can turn around.

The OP says that they are traveling at the same speed (since the firefighter's 2 steps of 3 feet is the same as the nurses 3 steps of 2 feet). The nurse, however, will get to turn around at exactly the 100' mark, while the firefighter has to turn around at the 102' mark. So, the nurse travels exactly 200' during the race, the firefighter travels 204'...

So...since the firefighter has to travel 4' further than the nurse, and they are going the same speed...the nurse will cross just before him.

[Prof. Templeton]

I'm working right now, and don't have much time to get into thinking everything through...however, at first thought, since the nurse runs 2 feet every step, she will evenly hit the 100 foot mark...but the firefighter will have 1 foot left where he would probably have to do a stutter step or something to hit that point...OR if he just kept running at his normal pace, he would have hit the 102 foot mark before being allowed to turn around, in which case, the nurse would win, because she traveled less distance.

For each leg of the race, the firefighter has to take 100/3 = 33.33 => 34 steps, or 68 steps total.

For each leg of the race, the nurse has to take 100/2 = 50 steps, or 100 steps total.

She takes 3 steps for every 2 of his, so, because 100/68 < 3/2, the nurse wins.

The OP states that every step was either 3 feet or 2 feet, depending on the person, and that the distance was just 200 feet (not 204). The race could have been 200 feet in just one direction and the outcome would have been the same. Trap Sprung. The OP doesn't say how it was done, just that it was.

[Guest]

Got it! (I think)

There is no relation to time in thier paces and thus impossible to tell who actually won.

E.G. The firefighter could take 100paces/min but the nurse only 1pace/min. In this the nurse could still take 3 steps to every 2 of the firefighters but would still lose bigtime.

[HoustonHokie]

The OP states that every step was either 3 feet or 2 feet, depending on the person, and that the distance was just 200 feet (not 204). The race could have been 200 feet in just one direction and the outcome would have been the same. Trap Sprung. The OP doesn't say how it was done, just that it was.

Exactly. Having to turn around makes the difference between 67 or 68 total steps for the firefighter, but the nurse still wins either way. Now, if they had traveled 204 feet (102 each way), that would be different - they would tie.

[Prof. Templeton]

Exactly. Having to turn around makes the difference between 67 or 68 total steps for the firefighter, but the nurse still wins either way. Now, if they had traveled 204 feet (102 each way), that would be different - they would tie.

But if every step is 3 feet there is no way the firefighter could take the extra step without going to 102 feet. Given these qualifications the runners either looped around the turning point never missing a stride or magically pivoted in mid-air if necessary, or employed some other means. 100 not being evenly divisable by 3 is not important to the solution.

[Guest]

A different take

The whole town was invited to watch this epic race. Men turned out to watch the nurse, women to see the firefighter. Weeks of promotion ensured that it was a huge crowd. But on the day, there was no tie, because there was no race. It was April fool's day and the nurse and the firefighter were safely tucked up in bed (although not necessarily together) chuckling at the mischief they had created

Am I right?

[Prof. Templeton]

A different take

The whole town was invited to watch this epic race. Men turned out to watch the nurse, women to see the firefighter. Weeks of promotion ensured that it was a huge crowd. But on the day, there was no tie, because there was no race. It was April fool's day and the nurse and the firefighter were safely tucked up in bed (although not necessarily together) chuckling at the mischief they had created

Am I right?

It was indeed April Fool's Day. However, a race was run and there was a winner and a mathematical solution can be found.

[plasmid]

Whoever was first off the starting line won? The OP doesn't say anything about their reaction times being equal.

[Guest]

Whoever was first off the starting line won? The OP doesn't say anything about their reaction times being equal.

oooohhhhh. dat makes sense.

i was thinking it was a fool race to trick everyone on april fools day.

[Guest]

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?

Since we had not been given any information on the speed of each racer except that the firefighter walk 3/2 feet per step, and that the nurse walk 2/3 feet per step.

So can we not assume that the time it takes for both racer to each take a step is the same, because it is not stated otherwise?

If so, then firefighter's time would be (in steps):

t = d/s = 200/(3/2) = 133.33

Whereas the nurse's time (in steps):

t = d/s = 200/(2/3) = 300 steps.

Therefore, the firefighter won.

[DudleyDude]

That if we assume that the winner has to touch ground once crossing the line to win, then we can look at it like this.

The nurse will win a 2 ft race (her first step goes only 2 ft, but she touches ground while the ff is still taking his first step)

The ff will win a 3 ft race

The nurse will win a 4 ft race

A 6 ft race will be a tie.

Using this logic, they both touch ground at the same time at the 198 foot mark.

That leaves a 2 ft race to the finish which the nurse will win.

This solution does make the assumption that steps are taken at a uniform speed by both racers.

[Prof. Templeton]

Whoever was first off the starting line won? The OP doesn't say anything about their reaction times being equal.

They were both seen to leave the starting line at the exact same time.

Since we had not been given any information on the speed of each racer except that the firefighter walk 3/2 feet per step, and that the nurse walk 2/3 feet per step.

So can we not assume that the time it takes for both racer to each take a step is the same, because it is not stated otherwise?

If so, then firefighter's time would be (in steps):

t = d/s = 200/(3/2) = 133.33

Whereas the nurse's time (in steps):

t = d/s = 200/(2/3) = 300 steps.

Therefore, the firefighter won.

133.33 steps is more then either would need to finish a 200 foot race.

That if we assume that the winner has to touch ground once crossing the line to win, then we can look at it like this.

The nurse will win a 2 ft race (her first step goes only 2 ft, but she touches ground while the ff is still taking his first step)

The ff will win a 3 ft race

The nurse will win a 4 ft race

A 6 ft race will be a tie.

Using this logic, they both touch ground at the same time at the 198 foot mark.

That leaves a 2 ft race to the finish which the nurse will win.

This solution does make the assumption that steps are taken at a uniform speed by both racers.

You can cross the finish line while still in mid-air.

[Guest]

but then she made 3 steps to his 2 steps.

does that mean that in the time it took the firefighter to take 2 steps, the nurse took 3?

[Prof. Templeton]

does that mean that in the time it took the firefighter to take 2 steps, the nurse took 3?

It means that in the time it took him to make 2 steps, she would make 3 steps in the same amount of time.

[Guest]

It was the first of April they were just fooling around

[Prof. Templeton]

It was the first of April they were just fooling around

There was a race, but it being on April 1st is a hint.

[Guest]

Given the age of your photograph, it appears the time when Prof was a young lad would be quite a long time ago. Does the year/era of this race matter?

[Guest]

At 198' both racers have their foot on the ground, the nurse made 99 complete steps while the Fire fighter made 66 complete steps.

There are only 2' left in the race. The nurse makes one final complete step and the front of her shoe is at the finish line.

The FF take one last step and is 66% of the way through as the Nurse's foot hits the ground.

At this point no one won yet since no one crossed the 200' mark. As the nurse picks up her foot to make another step, the FF's foot comes down to complete his 67th step and crosses the line first and sets his foot down at the 201' mark as the nurses foot is at appogee at he 201' mark.

FF wins

It could be that they were there to save lives maybe from a fire. "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."

[Prof. Templeton]

Given the age of your photograph, it appears the time when Prof was a young lad would be quite a long time ago. Does the year/era of this race matter?

The year/era of the race doesn't appear to matter much. A version of this was printed in late 19th century.

[CaptainEd]

The taller person of the two won the rice by leaning forward and breaking the plane of the finish line first--they had movie cameras in the late 19th century, a photo finish could show that unequivocally.

I don't see how April 1 fits in, though...so I'm expecting to be hoodwinked.

[DudleyDude]

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.