Teaser 2736: HS2
From The Sunday Times, 1st March 2015 [link] [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?
[teaser2736]
S2T2 
Jim Randell 12:00 pm on 17 September 2020 Permalink |
If the time at constant speed is AB minutes, then the total time is BA minutes, and:
So:
The maximum speed is 220 mph = 11/3 miles per minute.
From the velocity/time graph we get the total distance d is:
From which we see (A + B) must be divisible by 6, so (A, B) = (1, 5) or (2, 4), and d = 121.
A simple Python program can verify this:
Run: [ @replit ]
from enigma import (subsets, irange, div, printf) for (A, B) in subsets(irange(1, 5), size=2): d = div(121 * (A + B), 6) if d is not None: printf("d={d} [A={A} B={B}]")Solution: The journey was 121 miles long.
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