# The cyclists and the fly

CalJust
Posers and Puzzles 16 Oct '06 06:15
1. CalJust
It is what it is
16 Oct '06 06:15
Two cyclists (call them A and B) are on the same road, 60 km apart facing each other.

At the same moment they ride off towards each other, A at 10 km/hr and B at 20 km/hr.

A fly sits on B's nose and at the moment that he starts cycling, he flies off in the same direction (i.e. towards A) at 30 km/hr.

As soon as the fly reaches A, he turns around (again instantaneously) and flies back towards B. As soon as he reaches B he turns around again and flies back towards A, and so on until the two riders meet.

Question: What distance did the fly travel?
2. 16 Oct '06 09:19
60 km
3. 16 Oct '06 14:59
what if both cyclists are travelling at 10km/h
4. PBE6
Bananarama
16 Oct '06 15:10
Originally posted by aginis
what if both cyclists are travelling at 10km/h
90 km
5. 16 Oct '06 15:31
and in general

distance d and speeds A,B and C
6. 16 Oct '06 16:14
d.C/(A+B)
7. 16 Oct '06 16:35
i'd like to thank everyone for participating and i hope we never have to go through this problem again.
8. 16 Oct '06 16:41
Originally posted by aginis
i'd like to thank everyone for participating and i hope we never have to go through this problem again.
Well, the fly died in the crash anyway.
9. sonhouse
Fast and Curious
17 Oct '06 03:24
Originally posted by Mephisto2
Well, the fly died in the crash anyway.
A had a fly swatter and killed it halfway through so it only went 30 KmðŸ™‚
10. CalJust
It is what it is
17 Oct '06 05:52
Thanks, y'all.

In case aganis hasn't figured it out yet, all you do is find out the length of time the fly flew - which is the time it takes the cyclists to meet, i.e. 2 hours - and then multiply by its speed.

I know someone who worked it out as a series...

Here is a similar one:

Four bugs sit on the corners of a square of side one meter.

The bugs are alternating male and female, i.e. if the corners of the square are A,B,C & D, then A and C are male, B and D are female.

Each bug now starts to stalk the bug directly in front of it. As they do so, deviating neither to the right nor the left, they each describe a spiral that meets in the centre of the square.

I leave it to your imagination what happens at this spot. The question is, however, what is the length of the spiral that the bugs travelled?
11. 17 Oct '06 10:36
Originally posted by CalJust
Thanks, y'all.

In case aganis hasn't figured it out yet, all you do is find out the length of time the fly flew - which is the time it takes the cyclists to meet, i.e. 2 hours - and then multiply by its speed.

I know someone who worked it out as a series...

Here is a similar one:

Four bugs sit on the corners of a square of side one meter.

The ...[text shortened]... this spot. The question is, however, what is the length of the spiral that the bugs travelled?
The famous line is:

One day this problem was asked of the mathematician (I believe it was Stibitz) who quickly responded 60 km. The questioner (another mathematician), chuckled at the speedy response and said, "You're right. Most people take much longer to solve that problem because they solve it by summing each of the fly's flights until the crash." Stibitz responded, "That's how I DID do it."
12. CalJust
It is what it is
19 Oct '06 13:461 edit
Originally posted by Gastel
The famous line is:

One day this problem was asked of the mathematician (I believe it was Stibitz) who quickly responded 60 km. The questioner (another mathematician), chuckled at the speedy response and said, "You're right. Most people take much longer to solve that problem because they solve it by summing each of the fly's flights until the crash." Stibitz responded, "That's how I DID do it."
Hi Gastel - thanks for reminding me of that anecdote - however, it applied to the OTHER fly-and-cyclists problem!

Do you also know the short answer to this one?
13. 20 Oct '06 02:19
Originally posted by CalJust
Hi Gastel - thanks for reminding me of that anecdote - however, it applied to the OTHER fly-and-cyclists problem!

Do you also know the short answer to this one?
They're gay and stalk the one on the opposite so the 'spiral' is simply a straight line to the centre and is length ROOT(0.5). When they meet at the centre, the opposite sexes ignore each other completely and have at it with their opposite number.

Actually, I have never heard this one before (for heteroinsextivorous flies), but from an optimization point of view, even if they were chasing a fly in an adjacent corner, and no two flies were chasing either the same fly or each other, then they would follow this same curve as it would lead to the quickest mutual victory. If two flies chased the same fly, then the spirals would be more complex but would follow one edge for two flies (as they head directly toward each other) and meet in the middle. If two pairs of mutually attracting flies was the situation, then all flies would follow their edge and two orgies on opposite midpoints would be had. (Until they got tired of each other and needed to go out and 'discover' themselves with some slimy turd of a fly - if he dare comes near me I'll - nevermind that was a few marriages and long ago and I'm over it - the midpoint was fine for me - we had our laughs - but then the spirals started again - and she was headed for the other female - and then I found myself the target of the other male and my spiral was constrained by the damn 1 meter edge table and soon his bad breath was on my neck and ... )

I'm going for a drink. Later.