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Summer Maths Puzzles - Wednesday 14 August - Distance Dilemma

Distance Dilemma

This morning, the middle child foolishly asked the parents their least favourite question: "Are we nearly there yet.....?".  This inspired them to set the children the following challenge.

  • AA Architects and BB Bank lie at opposite ends of the same (straight) road. 
  • Archie works at AA Architects and Bianca works at BB Bank.
  • At 1pm Archie leaves AA Architects to drop off a letter at BB Bank and at the same time Bianca sets off from BB Bank to drop off a letter at AA Architects.
  • They meet for the first time at a distance a metres from AA Architects and for the second time at a distance b metres from BB Bank. 
  • Assuming that they each walk at a constant speed, how far, in terms of a and b, is AA Architects from BB Bank?

Please email your answers to deputy-director[at][dot]uk and remember to include your name (or the name of the group that you solved the puzzle with) so that we can publish it on our website if you are one of the first few to successfully solve the problem.  

Answers to all puzzles will be published at the end of the month. 

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons