Maths on the underground

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As I was on my way to catch the train home this evening, I received a text from a friend with the following question:

Two flagpoles, heights a and b, are separated by a horizontal distance d. The top of each flagpole is joined by a wire to the bottom of the other pole. At what height do the wires cross?

I solved it on the metropolitan line with a few minutes’ thinking and scribbling time. Let me know how you get on, and feel free to share your methods in the comments.

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2 Responses to “Maths on the underground”

  1. Tweets that mention Maths on the underground « Alison Kiddle's NRICH blog -- Topsy.com Says:

    […] This post was mentioned on Twitter by The NCETM and Nrich maths, Alison Kiddle. Alison Kiddle said: Yesterday's short blogpost with a maths problem can be found here: https://ajk44.wordpress.com/2011/01/27/maths-on-the-underground/ […]

  2. Edward Says:

    It depends. Are the flagpoles vertical? 😛

    Assuming they are, we obtain a pair of similar triangles (because the poles are parallel); letting h be the height of the crossing, we have that a : h :: b : b-h, thus a(b-h)=bh; solving gives h=ab/(a+b) which is the harmonic mean, ie. h=1/(1/a+1/b). Which is nice.

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