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Four friends built a colony for themselves. They built their own houses at different distances from each other. Chris lived 60km away from Alex. Darren lived 40km away from Bill. Chris lived 10km nearer to Darren than he lived to Bill. Can you find out how far was Darren's house from Alex?

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  • $\begingroup$ Welcome to Puzzling! This is a mathematics problem, not a mathematics puzzle. Puzzles should have some sort of crucial insight rather than just regular calculations - the mutilated chessboard is a great example of a math puzzle. $\endgroup$
    – Deusovi ♦
    Commented May 11, 2016 at 4:05

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In general, no; but if you're implying that

Alex, Bill, Chris, and Darren live on a straight line in alphabetical order

, then:

* AC = 60
* BD = 40
* BC - CD = 10

so:

* BC + CD = BD = 40
* 2 CD = 30
* CD = 15
* AD = AC + CD = 75

(And, for completeness:

AB = 35, BC = 25, CD = 15

.)

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Well,

No, I can't.
If Darren is 40km from Bill, and the only restriction on Chris' house is that it is 10km closer to Darren's than Bill's (ignoring Alex, since that won't affect it), then there are an infinite number of places (along a line that crosses the line from Bill to Darren) where Chris' house can be. From there, just put Alex's house 60km from any point on that line, in any direction. There's no way to know how far it is from Darren's.

But,

If they are all along a line, then there are two places Alex's house can be:
If Chris' house is 10km closer to Darren's than Bill's, then it has to be between them, since otherwise it would 40 km closer to one of them. That means it's 15km from Darren's and 25 km from Bill's. Then Alex's house can be either 45km past Darren's house or 35km past Bill's IMG the other direction, making it 75km from Darren's.

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    $\begingroup$ The "line that crosses the line from Bill to Darren" is known as a hyperbola. $\endgroup$
    – ffao
    Commented May 11, 2016 at 2:05
  • $\begingroup$ @ffao Whoa, whoa, it's only half a hyperbola. No need to be so hyperbolic! $\endgroup$
    – paste
    Commented May 11, 2016 at 2:36
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    $\begingroup$ ...and we don't even know that they live on a plane. $\endgroup$
    – Jonathan Allan
    Commented May 11, 2016 at 3:55

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