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N Is a Number

Age 11 to 14
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A group of N people holidaying in the seaside town A decided to visit their friends staying town B which is N km (kilometres) along the coast.

Some of the group walk along the cliff path at a steady N km an hour. The rest, one less in number than the walkers, go by car which (not counting stops) averages $10$ times the speed of the walkers.

The road is much longer than the cliff path.

map

Those in the car stop for N minutes for fuel, then N times as long as that for coffee, and are further delayed for N minutes by a flock of sheep. They finally reach town B one minute before the walkers.

How long is the road between towns A and B ?


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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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