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Leaving Las Vegas (Posted on 2003-04-14) Difficulty: 4 of 5
A courier pigeon departs Las Vegas for Reno at the same time as another courier pigeon departs Reno for Las Vegas. Both pigeons fly at constant speeds, although different from each other. They cross paths 2x miles from Las Vegas. After each arrives at their destination they immediately turn around, going back and forth without breaks. They cross paths the second time x miles from Reno.

Where will they cross paths the third time?

  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.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionPraneeth Yalavarthi2007-07-17 10:59:46
SolutionThe 3 solutionsJack Squat2004-01-15 15:24:02
re: my solutionCory Taylor2003-04-17 08:23:24
my solutionCory Taylor2003-04-17 08:19:18
Solutionre(2): solution--another solutionCharlie2003-04-14 05:56:00
Some Thoughtsdon't ask me howHank2003-04-14 05:42:40
Questionre: solutionfwaff2003-04-14 04:14:31
SolutionsolutionCharlie2003-04-14 03:28:56
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