FOR SMaRT PEOPLE (OR PEOPLE GOOD AT MATH)?

Question

this question NO ONE can figure out in my Trig class. and its 10 points extra credit so if anyone can help me out that would be so great (i need it)
There are four cottages on a straight road. The distance between Ted and Alice's cottages is 3 kilometers. Both Bob's and Carol's cottages are twtice as far from Alice's as they are from Ted's. Find the distance between Bob's and Carol's cottages in kilometers.

IF YOU EVEN HAVE AN IDEA OF HOW TO SOLVE IT, THAT WOULD BE GREAT.

Answer 1

You need a diagram

Alice ---- 3 Km ------ Ted ---- 3 Km ----- Bob and Carol

They must be together if they are on a straight road and are both as far from Alice and Ted.

Of course it could be like this

Alice - 2 Km - Bob - 1km - Ted - 3 km - Carol

So the answer is 4 Km or 0 Km

Answer 2

Bob and Carol's houses are either in the same place (and therefore zero miles apart), or they are four miles apart.

First, the "concept". Draw a number line....

---------------T------A--------------

Where could a cottage be that is twice as far away from Alice's as Ted's? Well, there could be one between the A and T, where B is 1/3 of the way from T to A, 1 km from T, 2 km from A. And there is another one C, to the left of T, another 3 km. That would mean C to T is 3 km, and C to A = 3+3 = 6 km. So your number line is....

------C- - - (3 k m) - - -T-(1km)-B- - (2 km) - -A--------------

And count the km to verify that B and C are 4 km apart.

Since we are in only one dimension, lets say Ted's house is at zero, and Alice's is at 3. Distance between Ted and Alice is | 3 - 0 | = 3.

I use |x| to mean the absolute value, and |x - y| to mean distance.

A house that is twice as far from 3 as from 0 could be written like this...

|x-3| = 2|x-0|

But solving this equation is tricky. Because of the absolute values, you have to consider three possible cases for x: there could be a solution (or not) in all three of them. First, when x>3, all absolute values in the equation are positive.

x-3 = 2x solves to x = -3. This is bad, because we assumed that x>3. What about if x<0, and both the abs. values are negative numbers??

-(x-3) = -(2x). This simplifies to x = -3, too. This is good, because we assumed that x<0. So there could be a house at x=-3. This is house C in our concept above.

But that leaves one more case. If 0 < x < 3, then the left abs. value is positive, the right one negative...

x-3 = -2x simplies to x = 1. That fits in our assumed range, so the other house (the B house in our concept) is at x=1. So, to recap.

We assumed T at 0, and A at 3. We found C at -3, and B at 1. The distance between B and C is |1 - (-3)| = 4.

This is a bit long and gory, but designed to please mean 'n' nasty Trig teachers like yours. This problem is a gem.

Answer 3

The houses are arranged in the order Alice, Bob, Ted, Carol (A, B, T, C)

Alice is 2km from Bob,
Bob is 1km from Ted
Ted is 3km from Carol

so bob and carol are 4km apart.

I just noticed that the houses had to be arranged with either bob or carol living between alice and ted in order for Bob and Carol to not have to live in the same house

here's a visual
Alice <--2--> Bob <-1-> Ted <---3---> Carol

Answer 4

Ted = 3 km to Alice
Bob = 6 km to Alice (3km to Ted * 2 =6)
Carol = 6 km to Alice (3km to Ted * 2 =6)
Bob = 12 km to Carol (3 km to Ted + 3 km to Alice + 6 km to Carol)

Answer = 12 km

Answer 5

12 kilometres. first is bobs then 3 k farther is teds, then 3 k is alice, then 6 k is carol.

Answer 6

bob and carol live together...so the answer is 0. it never says that they all live in different cottages.

Answer 7

how about 12 kilometers?

Answer 8

most likely 12 kilometers. im twelve and i figured that out

Answer 9

is there a diagram that came with the question?