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**Oculus8596****Banned**- From: Great Lakes,Illinois
- Registered: 2024-09-18
- Posts: 126

The Bermuda Triangle Karen is doing research on the Bermuda Triangle which she defines roughly by Hamilton.Bermuda; San Juan . Puerto Rico; and Fort Lauderdale, Florida.On her atlas Karen measures the straight-line distances from Hamilton to Fort Lauderdale, Fort Lauderdale to San Juan, and San Juan to Hamilton to be approximately 57 millimeters (mm ), 58 mm, and 53.5 mm respectively. If the actual distance from Fort Lauderdale to San Juan is 1046 miles.

approximate the actual distances from San Juan to Hamilton and from Hamilton to Fort Lauderdale.

I need to calculate the scale of the map.

58 mm/(1046 miles) = 1/18.03 miles per mm. This is the scale of the map.

Distance from Puerto Rico to Bermuda:

53.5 mm • 1/(1046) miles per mm is ≈ 2.97 miles.

Distance from Bermuda to Florida:

57 mm • 1/(1046) miles per mm is ≈ 3.16 miles.

It looks ok to me.

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 10,583

Does it? It shouldn't. Those mm measurements are all pretty close so the miles should be too. But you've got places so close you could walk/swim the distance.

I did it this way. What do you have to multiply 58 by to get 1046. answer =what it has become, divided by what it was.

multiplier = 1046/58

Bob

ps. Maths is supposed to represent the real world so any answer should pass the 'is it reasonable?' test.

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob

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**Oculus8596****Banned**- From: Great Lakes,Illinois
- Registered: 2024-09-18
- Posts: 126

Bob wrote:

Does it? It shouldn't. Those mm measurements are all pretty close so the miles should be too. But you've got places so close you could walk/swim the distance.

I did it this way. What do you have to multiply 58 by to get 1046. answer =what it has become, divided by what it was.

multiplier = 1046/58

Bob

ps. Maths is supposed to represent the real world so any answer should pass the 'is it reasonable?' test.

To approximate the actual distances from San Juan to Hamilton and from Hamilton to Fort Lauderdale, I can use the scale of Karen’s atlas.

First, I need to find out the scale of Karen’s atlas. I'll do this by comparing a distance on her map with its corresponding real-world distance.

The measured straight-line distances are:

1. From Hamilton to Fort Lauderdale: 57 mm

2. From Fort Lauderdale to San Juan: 58 mm

3. From San Juan to Hamilton: 53.5 mm

Given that the actual distance from Fort Lauderdale to San Juan is 1046 miles, I will calculate the scale using this known value:

Scale = Actual Distance / Map Distance

For example, Scale for “From Ft.Lauderdale To Puerto Rico”= (1046miles/58mm)=18miles/mm.

Now that I found our Scale, I will apply it in order estimate other two unknowns.

So now applying same formula as above,

Actual Distance between :

1. SanJuan-Hamilton=(53.5*18)mile ≈963 mile

2. Hamilton-FtLauderale =(57 *18 )mile≈1026 mile

Is this much better, Bob?

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