Two cyclists and a fly

[MarkFL]

Jim Bob and Ellie May live exactly 10 miles apart along a straight road, and they wish to ride their bicycles to meet because their kin are a feudin' and they must meet in private. They depart their homes at precisely the same time, and cycle towards one another each at a steady pace of 5 mph. At the precise moment Jim Bob commences to peddlin', a big horsefly takes off from the tip of his nose and travels 10 mph in a straight line towards Ellie May, and when it reaches her, lights on her nose and immediately travels back to Jim Bob, lights on his nose and goes back and forth betwixt the two young lovers until they meet.

What was the total distance traveled by the horsefly during its flights between Jim Bob and Ellie May?

 

[Rens]

5 miles

 

[MarkFL]

5 miles

No, the fly flew farther than 5 miles.

Now, the fly did end up files miles from where it began (so it's total displacement was in fact 5 miles), but I am asking for the total distance that the fly flew.

 

[Ackbach]

You could do the infinite summation, but it's much simpler to realize that the constant switching of direction of the fly doesn't change that it's essentially always covering 10 mph. As it'll take Jim Bob and Ellie May exactly one hour to meet, the fly will have covered 10 miles during that time.

 

[tango]

But the total distance may vary slightly because it may take less than a full hour for the fly to be crushed between two noses, given the size of the respective noses is not given.

 

[MarkFL]

You could do the infinite summation, but it's much simpler to realize that the constant switching of direction of the fly doesn't change that it's essentially always covering 10 mph. As it'll take Jim Bob and Ellie May exactly one hour to meet, the fly will have covered 10 miles during that time.

Yes, that's the trick to making this seeming difficult problem fall into place.

[unm]tango[/unm]...can I see you after class? :mischievous:

 

[Lamb]

The wind speed or direction was not given!

 

[MarkFL]

The wind speed or direction was not given!

Then we can neglect those factors...unless you wish to join [unm]tango[/unm] after class? :scared:

 

[Rens]

You could do the infinite summation, but it's much simpler to realize that the constant switching of direction of the fly doesn't change that it's essentially always covering 10 mph. As it'll take Jim Bob and Ellie May exactly one hour to meet, the fly will have covered 10 miles during that time.

Ooooh it took a while, but now I get it.

 

[psalms 91]

pesky fly

 

[ImaginaryDay2]

:smash: