Leaving Las Vegas (Posted on 2003-04-14)

	Submitted by Ravi Raja
Rating: 3.6667 (3 votes)
Solution:	(Hide)
First solve for x. Assume that the distance between Las Vegas and Reno is 1. Call 'r' the pigeon that starts in Reno and 'v' the pigeon that starts in Las Vegas. For any given amount of time the ratio of the distance traveled by 'r' to 'v' will be the same. This ratio at the first meeting is (1-2x)/2x. At the second meeting this ratio is (2-x)/(1+x). Equating these two ratios: (1-2x)/2x = (2-x)/(1+x). Then cross multiply. (1-2x)(1+x) = 2x(2-x) 1-x-2(x^2) = 4x - 2(x^2) 1-x = 4x 5x = 1 x = 1/5 So the first time they meet is 2/5 of the way from Vegas and the second time is 1/5 of the way to Reno. The easiest approach at this point is to just follow the two paths as the birds continue to fly and see where they meet. When 'v' has traveled 2/5 of the distance between Vegas and Reno to a point 3x the distance from Reno 'r' will have traveled 3/5 of this distance to 2x the distance from Reno. When 'v' has traveled another 2/5 he will be exactly in Vegas. Conventiently this is also where 'r' will be.

	Subject	Author	Date
	Puzzle Thoughts	K Sengupta	2023-05-12 22:38:54
	Solution	Praneeth Yalavarthi	2007-07-17 10:59:46
	The 3 solutions	Jack Squat	2004-01-15 15:24:02
	re: my solution	Cory Taylor	2003-04-17 08:23:24
	my solution	Cory Taylor	2003-04-17 08:19:18
	re(2): solution--another solution	Charlie	2003-04-14 05:56:00
	don't ask me how	Hank	2003-04-14 05:42:40
	re: solution	fwaff	2003-04-14 04:14:31
	solution	Charlie	2003-04-14 03:28:56