Two People, One Fly: How Far Will It Fly?

[TSN79]

Two people live 20 km from each other. They start cycling towards each other with a speed of 10 km/h. A fly starts from one of them and flies to the other person and then back to the first person. It has an average speed of 15 km/h. It continues to do this until the two people meet. How far will the fly have flown when the two people finally meet? Apparently this has one very complex solution as well as being a simple grade school/high school problem, but I'm having trouble seeing the simplicity I think...abyone?

Could it be that the answer is indeed 15 km...? Since it takes the two people 1 hour to come half way and meet up, and the fly would have been flying constantly at 15 km/h for indeed 1 hour, so it has flown a total of 15 km...?

 

[moose]

I posted a reply in the other thread, in brain teasers.

I think that the answer is yes, it is 15km since it is moving 15km/h for an hour.

 

[thepatientmental]

Yes, you are correct. The fly will have flown a total distance of 15 km when the two people finally meet. This can be seen by breaking down the problem into smaller distances and time intervals.

First, let's consider the distance between the two people when they start cycling towards each other. This distance is 20 km and they are both traveling at a speed of 10 km/h. Therefore, it will take them 2 hours to meet at the halfway point.

Now, let's look at the fly. It starts from one person and flies to the other person, a distance of 20 km. Since it has an average speed of 15 km/h, it will take the fly 20/15 = 4/3 hours to complete this journey.

But wait, the two people will meet at the halfway point in 2 hours, so the fly still has 4/3 - 2 = 2/3 hours left to fly. During this time, the fly will cover a distance of 2/3 * 15 = 10 km.

So, in total, the fly will have flown a distance of 20 km + 10 km = 30 km when the two people finally meet. But since the fly has to return to the original person, it will fly a distance of 30 km + 30 km = 60 km in total. However, if we only consider the distance it has flown before the two people meet, it is indeed 15 km.

This problem may seem complex at first, but breaking it down into smaller distances and time intervals can help us see the simplicity behind it.