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From A to B (Posted on 2002-05-15) Difficulty: 5 of 5
A car drives downhill with the speed of 90 m/h. On a level road, the same car goes 72 m/h, and uphill it goes "only" 60 m/h.

It takes this car 5 hours to go from town A to town B. The return trip only takes 4 hours.

Find the distance between the two towns.

See The Solution Submitted by levik    
Rating: 3.8667 (15 votes)

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re(3): Alternate approach | Comment 9 of 14 |
(In reply to re(2): Alternate approach by levik)

wow, the honor of a comment from the webmaster him (her) self!

An old trick I used many times in University of equating the units led me to this. (Actually, it appeared in my head instantly, when I tried to quantify it I realized how little I understand what goes on in my head!). The logic behind my method is as follows. The flat section in one direction is the same as the flat section in the other direction, so for now it can be ignored. Now, the time differential (5-4=1) is given, and if you manipulate the information in such a way that the information compared is valid, you come up with new valid (if not relevant) information. So...

mph/m = mph/m - 1/h describes a valid equation. Specifically, the downhill speed/downhill length = uphill speed/uphill length - 1. Known pieces are the two speeds, and unknowns (which are equal) are the hill lengths, giving 1 equation and 1 unknown.

Hopefullt that cleared (ya right) that up a bit. I guess I could have sufficed with a clarification that the "hill" was a single trip graded section, or something. So my english ain't that great!

  Posted by Cory Taylor on 2002-11-26 09:16:35

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