are any really intelligent people out there willing to try the question that has stumped my friends for weeks?

Question

Jordan and Manuel are on the track and field team at school. Running around the track one day, Jordan ran 444m and Manuel ran 777m. They both ran an even number of times around the track. How far around is the track?

***Good Luck!!!

Answer 1

dont know

Answer 2

I think sometimes "even number" means "whole number", like when I have seen people say "21 can be divided evenly by 3". We know what that means, and nobody would say "wrong, it can only be divided oddly by 3". So the track could be 111m around. Jordan ran an even 4 times around it, and Manuel ran an even 7 times around. This is using "even" to mean an exact or level 7 times, not 7-and-a-bit or almost-7.

Actually solving the problem for the given numbers is interesting. If 444m and 777m are both a whole number of rounds, then so is their difference 333m. If 444m and 333m are both a whole number of rounds, then so is their difference 111m. Now we can stop, because 333m is a multiple of 111m. This sequence lets you find the "greatest common divisor" without finding any other divisors, so it is better when the numbers are really big.

Answer 3

The ratio off Jordan's laps to Manuel's laps is 4/7.

So, they could run 4 laps and 7 laps but those are not both even numbers so multiply both by 2 to get 8 laps and 14 laps.
That will work and gives a distance around the track of 55.5m.

You could, of course, try 16 and 28 or 32 and 56 but the track starts to get a little small.

So your answer is 55.5m

Answer 4

I think we'd need to know how many laps they ran to give you a straight answer... but I'm guessing that Jordan was on the inside and Manuel was on the outside, so in the center of the track they would have ran approximately 610 m.

Answer 5

At 55.5 M around Jordan ran around it 8 times and Manuel ran around it 14 times. That's the largest the track can be. If it was 27.25M You can double the number of laps, still even numbers and so on.

Answer 6

Let x be the track length

Clearly 444 = x * (2k) for some positive integer k

777 = x * (2m) for some positive integer m

taking the ratio

m/k = 777/444 = 7/4

So m = (7/4) k

k then must be a multiple of 4. since m must be an integer.

So that k = 4n where n is a positive integer

So that 444 = x * (2k) = x * (8n)

So x = 444/(8n) = 55.5/n

For some positive integer n. (which is the most you can know about x given this information.)

EDIT

i wonder if this is some smart *** answer

Answer 7

Jordan -> 8 laps
Manuel -> 14 laps

55.5m

Answer 8

55.5 m is one possible answer they would run around it 8 and 14 times respectively. There are other answers, for example 80 and 140 times around with 5.55 m track. Your friends are dumb I fear. Any pair of even #'s with a ratio of 1.75 between them would work.

Answer 9

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Answer 10

Too many answers. The inside lane could be 444m round, whilst the outside lane could be 777m so its possible it could be once. Or if the inside was 222m round it could be twice and the outer lane would be 388.5m round.........

Answer 11

There isn't enough info to get one answer, but 55.5m and 27.75m are both acceptable and possible answers