Two bikes and one fly?
Two people are riding their bikes towards each other. They are both travelling at 10km/h. There is a fly that starts at the handle of the first rider, flies to the second, and turns back to go to the first and repeats this action at 15km/h until the bikers meet. If the bikers were 20km apart to start off with, how much distance did they fly travel?
Ok, some of you might have seen this question before. That is why I am giving best answer to the first answerer who can provide 2(TWO) methods to solve this problem. Good luck!
“Do it for honor!”
For the first method:
The bicylists are heading towards each other at 20km/h, so they travel for one hour. The fly, at 15 km/h, travels 15 km.
As for the second method, forget it. I’m not summing the infinite series; that’s too much headache for a lousy 10 points. Von Neumann I’m not.
***Bah! If you insist!***
On the first trip of the fly, it travels x1 km at 15 km/h while the bicyle travels (20 – x1) at 10 km/h toward it. The times are equal, so x1/15 = (20 – x1)/10, 10×1 = 300 – 15×1, 25×1 = 300, x1 = 12 km. The 2nd bicycle has traveled 8 km, but so has the 1st bicycle. They are now 4 km apart.
On the second trip of the fly, it travels x2 at 15 and the bicycle travels (4-x2) at 10, so x2/15 = (4-x2)/10, 10×2 = 60 – 15×2, 25×2 = 60, x2 = 2.4 km. The bicycles are now 0.8 km apart.
Every time the fly turns around (magically taking no time at all to do it), it will travel 1/5 of the distance it just finished. The sum of these distances is 12* (1 + 1/5 + (1/5)² + …). The sum of the infinite series is 1/(1-(1/5)) = 5/4.
5/4 * 12 = 15 km.
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