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Chapter 1: Problem 111

The longest river in the world is the Nile River with a length of 4145 mi. How long is the Nile in cable lengths, meters, and nautical miles? Use these exact conversions to help solve the problem: $$\begin{aligned} 6 \mathrm{ft} &=1 \text { fathom } \\ 100 \mathrm{fathoms} &=1 \text { cable length } \\ 10 \text { cable lengths } &=1 \text { nautical mile } \\ 3 \text { nautical miles } &=1 \text { league } \end{aligned}$$

Short Answer

Expert verified
In summary, the Nile River is approximately 36,476 cable lengths, 3,647.6 nautical miles, and 1,995,234.91 meters long.

Step by step solution

01

Convert miles to fathoms

To convert the length of the Nile River from miles to fathoms, we need to use the following conversion: 1 mile = 880 fathoms Now, we can calculate the length of the Nile in fathoms by multiplying its length in miles by the conversion factor: \(Length_{fathoms} = Length_{miles} × Conversion\_factor\) \(Length_{fathoms} = 4145 × 880 \)
02

Calculate the length in fathoms

Now let's multiply the length in miles by the conversion factor to get the length in fathoms: \(Length_{fathoms} = 4145 × 880 = 3647600 \text{ fathoms}\) The length of the Nile River is equal to 3,647,600 fathoms.
03

Convert fathoms to cable lengths, nautical miles, and meters

Now that we have the length in fathoms, we can use the given conversions to find the length in cable lengths, nautical miles, and meters: 1 cable length = 100 fathoms 1 nautical mile = 10 cable lengths 1 meter = 1.8288 fathoms (approximately) To convert fathoms to cable lengths, nautical miles, and meters, we'll use the following formulas: \(Length_{cable\_lengths} = \frac{Length_{fathoms}}{100}\) \(Length_{nautical\_miles} = \frac{Length_{fathoms}}{100 × 10}\) \(Length_{meters} = \frac{Length_{fathoms}}{1.8288}\)
04

Calculate the length in cable lengths, nautical miles, and meters

Now, let's use the formulas from Step 3 to find the length of the Nile River in cable lengths, nautical miles, and meters: \(Length_{cable\_lengths} = \frac{3647600}{100} = 36476 \text{ cable lengths}\) \(Length_{nautical\_miles} = \frac{3647600}{100 × 10} = 3647.6 \text{ nautical miles}\) \(Length_{meters} = \frac{3647600}{1.8288} ≈ 1995234.91 \text{ meters}\) So, the length of the Nile River is approximately: - 36,476 cable lengths - 3,647.6 nautical miles - 1,995,234.91 meters

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