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N Is a Number

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.


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 ?