Help with Chain-Conversion Homework

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SUMMARY

The discussion centers on a homework problem involving the conversion of lengths measured in Smoots to Willies and Zeldas, using the Harvard Bridge as a reference. The correct conversion from 47 Smoots to Willies is established as approximately 57.198 Willies, based on the ratio of 212 Smoots to 258 Willies. However, the conversion to Zeldas presents challenges, with the participant calculating approximately 47.887 Zeldas but questioning the accuracy due to perceived inconsistencies in the provided graph ratios. The issue arises from the understanding that Zeldas do not necessarily start at zero, complicating the conversion process.

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Homework Statement



The problem is as follows:

Harvard Bridge, which connects MIT with its fraternities across the Charles River, has a length of 364.4 Smoots plus one ear. The units of one Smoot is based on the length of Oliver Reed Smoot, Jr., class of 1962, who was carried or dragged length by length across the bridge so that other pledge members of the Lambda Chi Alpha fraternity could mark off (with paint) 1-Smoot lengths along the bridge. The marks have been repainted biannually by fraternity pledges since the initial measurement, usually during times of traffic congestion so that the police could not easily interfere. (Presumably, the police were originally upset because a Smoot is not an SI base units, but these days they seem to have accepted the units.) The figure shows three parallel paths, measured in Smoots (S), Willies (W), and Zeldas (Z). What is the length of 47.0 Smoots in (a) Willies and (b) Zeldas?

I have attached the graph with the necessary information as an attachment.

Homework Equations


The Attempt at a Solution



The answer to convert from Smoots to Willies is pretty simple:
the ratio of S to W: 212S / 258W = 47S / xW , in which x came out to be approximately 57.198.

This was the correct answer for part a, however, when I try to do the same thing from Smoots to Zeldas or from Willies to Zeldas, the answer is wrong.

212S / 216Z = 47S / xZ, x = 47.887Z

or

258W / 216Z = 57.198W / xZ, x = 47.887Z

I assume it is wrong because the ratio of the graph is wrong (at 32S = 60Z, yet at 212S = 216Z), or I am reading the graph wrong. I am having trouble finding 47 Smoots in terms of Zeldas. Keep in mind the answer is accepted with +- 2% error.
 

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The graph is not wrong, it's just that Zeldas don't necessarily start at zero.
 

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