how many telegraph posts did holmes count?

extract from "Silver Blaze" - Memoirs of Sherlock Holmes

“We are going well,” said he, looking out of the window and glancing at his watch. “Our rate at present is fifty-three and a half miles an hour.”
“I have not observed the quarter-mile posts,” said I.
“Nor have I. But the telegraph posts upon this line are sixty yards apart, and the calculation is a simple one.”
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the question is "how many telegraph posts did holmes count?"

we know that 1 mile = 1760 yards

60 yards = 1 telegraph post
1760 yards = 1760/60 telegraph posts
= 29.33 telegraph posts


1760 yards per hour = 29.33 telegraph posts per hour, i.e.,
1 mile per hour = 29.33 telegraph posts per hour
53.5 miles per hour = 53.5 x 29.33 telegraph posts per hour
= 1569.155 telegraph posts per hour
= 1569.155/60 telegraph posts per minute
= 26.15 telegraph posts per minute (approximately)
= 27 telegraph posts per minute (approximately)

so, holmes must have counted about 27 telegraph posts.

Interesting....a little bit random....but interesting!

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Originally Posted by Reichenbach

Interesting....a little bit random....but interesting!

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what did you mean by random?

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Originally Posted by holmesian

so, holmes must have counted about 27 telegraph posts.

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That is assuming that he observed for exactly a minute.

He could as easily have counted poles for a longer period in order to derive a more accurate result, or even have extrapolated from a shorter period.

Or indeed, he could have timed the appearance of a fixed number of poles (perhaps 29.33 of them, an exact mile) and calculated from there, fixing the distance rather than the time period.

I don't believe the book states how long he was counting poles. Apart from that, I can't fault your mathematics.

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Originally Posted by Xamonas Chegwe

That is assuming that he observed for exactly a minute.

He could as easily have counted poles for a longer period in order to derive a more accurate result, or even have extrapolated from a shorter period.

Or indeed, he could have timed the appearance of a fixed number of poles (perhaps 29.33 of them, an exact mile) and calculated from there, fixing the distance rather than the time period.

I don't believe the book states how long he was counting poles. Apart from that, I can't fault your mathematics.

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yeah, i assumed that he watched for 1 minute. from the story it seems that he was looking out the window for a very short time. (“We are going well,” said he, looking out of the window and glancing at his watch.) that's why i assumed that he looked out for a minute.

but of course you are right too. he could have been counted poles for a longer period of time.