Remember this?

A hiker walks from one town to another. On the first day she covers one fifth of the total distance. The next day she covers a quarter of what is left. The following day she covers two fifths of the remainder and on the fourth day half of the remaining distance. She now has 25 miles left. How many miles has she travelled?

Good luck! You might want your calculator for this one…

Vel.

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April 19, 2010 at 9:43 pm

Such messy numbers (well, they’re nice as fractions, but still). I get 138.89 (or 138 8/9) miles.

April 20, 2010 at 8:46 am

I get 138.89 as well. Was hard to remember how to do these things, and im sure i didnt take the easiest route

Would like the full step-by-step from someone else though.

April 20, 2010 at 8:49 am

edit: 138.89 is the total distance to hike. Since the hiker still has 1/2 the distance to go (25 miles) the actual distance traveled is 113.89 miles.

April 22, 2010 at 6:00 am

Damn, missed that part :(.

April 22, 2010 at 4:06 pm

I’d put it as the hiker has traveled 41*25/9 miles, but then I suspect I’m weird.

Out of curiosity, because only as I hit the last step did I realize other people might not think of it this way: how did y’all solve it?

I did x(1-1/5-1/5-2/5*3/5+(1/2*(1-(2/5+2/5*3/5)))=25, simplified that down to 9x/50=25, which meant that x/50=25/9. Since what I really wanted was 41x/50, I just did 41*(x/50)=41*(25/9), or 113 and 8/9ths, as everyone else got.

Though, pedantic math language note to the first poster: I’d say your answer for the total distance as “138 and 8/9 (or about 138.89)”, since the version that isn’t an improper fraction is the one that’s the approximation, while 138 and 8/9 is exact. Of course, this is all assuming we don’t need to worry about sigfigs, which an entirely different mess under which we’re all probably wrong (I think technically the answer would be “100 miles” or “110 miles” under that depending on how you wanted to read significances, unless the last figure of 25 has more implied significance than we’re given it as).

May 11, 2010 at 1:31 pm

Oh man, I only have her traveling 79.8177 or so miles. And that number isn’t very pretty at all. I fear my chart of lines getting smaller and smaller and variable substitutions have failed me. π

May 11, 2010 at 2:42 pm

The answer is here, Mishaweha: https://veliaf.wordpress.com/2010/04/23/the-weekly-warlock-wind-up-hiking-answer/

π