0
$\begingroup$

This is just to confirm my idea on how to do this problem:

On a map, Cynthia lives $1$ mile east & $1.5$ miles south of a school. Charles lives $2$ miles west & $0.8$ miles south of the same school. How far apart (in miles) do they live from each other?

So I thought:

Cynthia lives $2.5$ miles from school. Charles lives $2.8$ miles from school.

But they are not driving to school. They are driving to each other. Therfore:

Cynthia lives $3$ miles from Charles.

This soultion was way too easy so I did not want to trust myself with this.

Could it perhaps be instead:

$1.5-0.8 = 0.7 => 3.7 \text{ miles}?$

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    You should probably apply the Pythagorean theorem somewhere.2012-07-01

1 Answers 1

2

enter image description here

Can you figure out the distance from the picture above by making use of the fact that the red triangle is a right angled triangle?

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    Doesnt that equal 3.7?2012-07-01
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    Nope. We can walk along the short past connecting Charles and Cynthia. Can you compute the distance?2012-07-01
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    I seem to be having difficulty understanding. Doesnt he still have to drive down .7 and over 3 miles?2012-07-01
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    @Michael No. Typically in problems like these it means the shortest distance between them i.e. in this case the distance of the hypotenuse of the right triangle.2012-07-01
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    Michael, the question asks how far apart they live, not how far they have to drive. Unless there's some good reason to do otherwise, I'd interpret "how far apart do they live" to mean, what is the straight-line distance between them? And that's the question Marvis is answering.2012-07-01
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    I understand the straight line. But he would still be travailing 3 miles2012-07-01
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    @Michael Assume that there is a road from Charle's home to Cynthia's home along the straight line connecting their houses. Then it is not $3$ miles. It is definitely more than $3$ miles.2012-07-01
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    But even the short path he is still travailing 3 miles and .7 down over the course of the road.2012-07-01
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    @Michael Why don't you find the length of the hypotenuse of the right triangle?2012-07-01
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    3.08. Correct??2012-07-01
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    @Bill Yes. So $3.08 < 3 + 0.7$ right? Hence, the answer is that they live $3.08$ miles apart.2012-07-01