Easy or hard puzzle? Cant decide.

[Tarrantula]

Got a puzzle for everyone.. I think I have it solved.. but it depends on how you look at it. What you do think??


"After the new freeway was built, I could no longer use the gravel road that ran due north from my house to get to my favourite lake. Instead, I now either have to go due east to Underville to use the underpass there, and then straight on to the lake, or else due west to Overtown, over the overpass there and then straight on to the lake.

Driving to the lake via Underville is twice as far as it was on the old gravel road. The other way, via Overtown, is three times as far as it was going straight north. The distance between Underville and Overtown is 39 km longer than it was from my house to the lake on the old gravel road.

How far was it from my house straight north to the lake?"

GO!:banghead:

[Awd-Tsi]

:whocares:

problem is worded weird, maybe draw a little drawing

[bspot]

x = house to lake

house is x from Underville and 1.5 x from Overtown.

so Overtown is 1.5x + x from Underville= 2.5x

2.5x = 39km + x

x= 26km

I just did your math homework. You're welcome :D

[colinxx235]

9.75km

[Tarrantula]

Originally posted by bspot
x = house to lake

house is x from Underville and 1.5 x from Overtown.

so Overtown is 1.5x + x from Underville= 2.5x

2.5x = 39km + x

x= 26km

I just did your math homework. You're welcome :D

Yeah, thats for sure wrong. draw it out next time.

[colinxx235]

hmmm actually that problem is worded strange, not sure if my original answer is correct or not...

[Tarrantula]

yeah, if you think of it as two triangles... its fucking hard..

[colinxx235]

well i've come to two different solutions depending on how you approach the wording. the more I think about it my new answer would be 19.5km.

I can make an analogy to drawing a trident roughly (obsiously one being spaced out 2x)


if you take the wording as still needing to go X distance north regardless of east or west,

you would have something like this

X X X
|__|____|
X 2X

so the final math would break down into

3x = x + 39

hmmm beyond deletes the spaces i've created with the X's to make it legible... oh well

x= 19.5km...

hopefully that brutal attempt at a diagram is understandable haha

[Tarrantula]

Originally posted by colinxx235
well i've come to two different solutions depending on how you approach the wording. the more I think about it my new answer would be 19.5km.

I can make an analogy to drawing a trident roughly (obsiously one being spaced out 2x)


if you take the wording as still needing to go X distance north regardless of east or west,

you would have something like this

X X X
|__|____|
X 2X

so the final math would break down into

3x = x + 39

hmmm beyond deletes the spaces i've created with the X's to make it legible... oh well

x= 19.5km...

hopefully that brutal attempt at a diagram is understandable haha

this is the first answer i came too.. what if you think of it as two triangles though? aka - your end points are the top of the north road...

lake
/|\
/x| \
/__|__\
x+39

[Feruk]

Originally posted by colinxx235
well i've come to two different solutions depending on how you approach the wording. the more I think about it my new answer would be 19.5km.

I can make an analogy to drawing a trident roughly (obsiously one being spaced out 2x)


if you take the wording as still needing to go X distance north regardless of east or west,

you would have something like this

X X X
|__|____|
X 2X

so the final math would break down into

3x = x + 39

hmmm beyond deletes the spaces i've created with the X's to make it legible... oh well

x= 19.5km...

hopefully that brutal attempt at a diagram is understandable haha

Wrong. It's a triangle solution. To assume going left is X left and then X up is NOT anywhere in the question. ONLY way that the question is solveable is if you assume you have to go to the SAME end spot on the lake because you can't assume the lake has the same perpendicular shape throughout.

I'll write out the solution...

[JfuckinC]

i get 19.5 too, same kinda idea as colin if undertown is 2x as long as original, then the route to undertown is the length of the route to the lake, plus that length north.. so the route to undertown and the route due north has to be half of 39, so that the route to overville is eqaul to that to the other half.

[colinxx235]

yah I thought of the triangle thing as well... which would make it nasty, its hard to tell from the wording if the lake matches all due north of both the origin and both over/underpass or if it.

i'll try some math on the triangle and edit it with what i can find... fun way to distract from controls homework...

[z24_wheels]

9.75 is correct I think.

Solve 2x + 3x = x+39

[Feruk]

FIRST triangle:
Distance from house to lake on gravel road = x
East to Underville = a
Underville to lake = 2x-a

SECOND triangle:
Distance from house to lake on gravel road = x
West to Overville = b
Overville to lake = 3x-b

DRAW them out. You now have 3 unknowns, meaning you need 3 equations to solve:
1) a + b = x + 39
2) x^2 + b^2 = (3x-b)^2 (right triangle)
3) x^2 + a^2 = (2x-a)^2 (right triangle)

Solve for x. I solved it for you, but you'll have to do the math.

[Feruk]

Originally posted by z24_wheels
9.75 is correct I think.

Solve 2x + 3x = x+39

Reading fail. 2x = distance to lake, 3x = distance to lake BUT x + 39 = distance between underville and overville, TOTALLY UNRELATED to distance to lake.

[z24_wheels]

No, I am wrong. You do need to think of it as a triangle and start doing trig.

[colinxx235]

my new answer is...

so fashion your triangle as before.

so perimeter of first triangle should be 3X
second triangle will be 4x
first : c= (2x-b)
second: c= (3x-b)
x^2 + b^2 = c^2
this gives you b (the bottom side)
for the first of b = 3/4X
first the second b = 4/3X

so your total on the bottom is 25/12X

25/12X = X + 39

X = 36km

so yes, lake was 36km north from his house. hopefully someone else gets the same solution as me.

[arian_ma]

You will have 5 equations and 5 variables at the end. I came up with this:

_____/_______|________\
____/________|_________\
_D_/_________|___X______\ _B
__/__________|___________\
_/___________|____________\
/____________|_____________\
_____C______________ A


A+B=2X Via underville is 2x as far
C+D=3X Via overville is 3x as far
A+C=39+X

D^2=C^2+X^2
B^2=A^2+X^2

Do some linear algebra folks

[Tarrantula]

36km is the answer my co-worker just provided me.. seems to work out perfectly :D

NICE WORK BEYOND MATH TEAM!

[thepyrofish]

Originally posted by Feruk
FIRST triangle:
Distance from house to lake on gravel road = x
East to Underville = a
Underville to lake = 2x-a

SECOND triangle:
Distance from house to lake on gravel road = x
West to Overville = b
Overville to lake = 3x-b

DRAW them out. You now have 3 unknowns, meaning you need 3 equations to solve:
1) a + b = x + 39
2) x^2 + b^2 = (3x-b)^2 (right triangle)
3) x^2 + a^2 = (2x-a)^2 (right triangle)

Solve for x. I solved it for you, but you'll have to do the math.

This is what I was trying to do, but math class was a long time ago and I have real work to do... I gave up.
http://imgur.com/e8nse.png

[Feruk]

Originally posted by colinxx235

first : c= (2x-b)
second: c= (3x-b)


Your two formulas cancel out eh? If you use those, 2x=3x, so if you solve it your way, X=0 :)

[Tarrantula]

Originally posted by Feruk


Your two formulas cancel out eh? If you use those, 2x=3x, so if you solve it your way, X=0 :)

two different c's.. two triangles.

[benthe8track]

36km is correct.

[benthe8track]

wtf.. This isn't my account. How did I get into someone else's account? weird...

[Awd-Tsi]

Better question than the original, is why are you guys doing math on your free time? Play some halo or something

[dexlargo]

36 is the right answer, but I don't quite follow all the steps others have taken. Here is how I got there using this diagram to define the variables:

Originally posted by arian_ma

_____/_______|________\
____/________|_________\
_D_/_________|___X______\ _B
__/__________|___________\
_/___________|____________\
/____________|_____________\
_____C______________ A

we know:

a+b=2x (going east is 2x as far)
b=2x-a (isolating b)

c+d=3x (going west is 3x as far)
d=3x-c (isolating d)

Then we know from the Pythagoras theorem:

x^2 = d^2 - c^2
so, let's plug in the isolation of d:
x^2 = (3x-c)^2 - c^2
x^2 = (3x-c)(3x-c) - c^2
x^2 = (9x^2 - 6cx + c^2) - c^2
x^2 = 9x^2 - 6cx
6cx = 8x^2
c = 4x/3

and also from the Pythagoras theorem

x^2 = b^2 - a^2
x^2 = (2x-a)^2 - a^2 (again, plugging in the isolation of b)
x^2 = (2x-a)(2x-a) - a^2
x^2 = (4x^2 - 4ax + a^2) - a^2
x^2 = 4x^2 - 4ax
4ax = 3x^2
a = 3x/4

Then we know that the distance between overtown and undertown is:

a+c=x+39
3x/4 + 4x/3 = x+39 (subbing in a and c as determined above)
25x/12 - x = 39
13x/12 = 39
x = (12/13) * 39
x = 36

[rob the knob]

is this caused by canadian indian reserve?

(just joke. not serious)

[banned3x]

Originally posted by rob the knob
is this caused by canadian indian reserve?

(just joke. not serious)



hahhahah that's what I was thinking. He's looking for the fastest way to the grey eagle casino