Sunday Times Teaser 2736
by Alan Bergson
Published: 1 March 2015 (link)
Last night I dreamt that I made a train journey on the HS2 line. The journey was a whole number of miles in length and it took less than an hour. From the starting station the train accelerated steadily to its maximum speed of 220 mph, then it continued at that speed for a while, and finally it decelerated steadily to the finishing station. If you took the number of minutes that the train was travelling at a steady speed and reversed the order of its two digits, then you got the number of minutes for the whole journey.
How many miles long was the journey?
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Brian Gladman permalink1234567891011121314151617181920# The average speed during acceleration/deceleration is (11/6)# miles per minute, half that at constant speed. So the total# distance is (11/6).(t_acc&dec + 2.t_constant), which can be# expressed as (11/6).(t_total + t_constant). If the digits in# the two numbers are a and b, this gives 121.(a + b)/6. So# a + b = 6 and the distance is 121 miles.soln = set()# 'total' is the total journey timefor total in range(10, 60):# reverse the digits to find the time at constant speedconstant = 10 * (total % 10) + total // 10if constant < total:distance, rr = divmod(11 * (total + constant), 6)if not rr:soln.update([distance])for distance in soln:print('The journey was {} miles long.'.format(distance))
