Enigma 1105: Road ants
24 July 2017
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From New Scientist #2261, 21st October 2000
Take a large sheet of paper and a black pen and draw a rectangle ABCD with AB = 10 metres and BC = 2 metres. Now draw lines to divide your rectangle into small squares, each of side 1 centimetre. Place your diagram so that A is due north of D and B is east of A. In each small square draw the diagonal that goes from northwest to southeast. Let P and Q be the mid-points of AD and BC, respectively. Then there is a black line PQ; remove it and replace it by a red line.
Amber is a small ant who can walk along the black lines in your diagram. North of PQ she covers a centimetre in 1 minute, but south of PQ she can cover a centimetre in 30 seconds. She is to walk from C to A and she chooses the quickest route.
1. How long does Amber take on her journey? Give the time, to the nearest second, in hours, minutes and seconds.
Ben is another ant who walks along the black lines. North of PQ he goes at the same speed as Amber, but not south of PQ. The fastest time for Ben to get from C to A is 24 hours.
2. South of PQ, how long does Ben take to cover a centimetre? Give the time, to the nearest second, in minutes and seconds.