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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?


Entry to this puzzle is now closed.  Congratulations to the following for some great answers: 

  • Junyang Wang
  • Ali Raad
  • Niall Moran and Jenny McSharry
  • Benjamin Dadoun
  • Emily Lies and Jan Ricken
  • Soham Sud
  • Chengyuan Li
  • Evgeny Mirkes
  • Patrick Luo
  • Ben Katz
  • Ben Xiao


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