# Thread: Number Line With r, s, and t

1. ## Number Line With r, s, and t

On the number line, if r < s, if p is halfway between r and s, and if t is halfway between p and r, then (s - t)/(t - r) =

A. 1/4
B. 1/3
C. 4/3
D. 3
E. 4

The book tells me that the distance from r to t is x, the distance from t to p is x and the distance from p to s is 2x.

The book concludes that
(s - t)/(t - r) = (x + 2x)/x, which of course is 3.

I do not understand the logic here.

2. ## Re: Number Line With r, s, and t

I would let:

$\displaystyle s-r=4d$

Then:

$\displaystyle p-r=2d$

And:

$\displaystyle t-r=d$

Subtracting the third equation from the first, we obtain:

$\displaystyle s-t=3d$

Hence:

$\displaystyle \frac{s-t}{t-r}=\frac{3d}{d}=3$

3. ## Re: Number Line With r, s, and t

Originally Posted by harpazo
On the number line, if r < s, if p is halfway between r and s, and if t is halfway between p and r, then (s - t)/(t - r) =

A. 1/4
B. 1/3
C. 4/3
D. 3
E. 4

The book tells me that the distance from r to t is x, the distance from t to p is x and the distance from p to s is 2x.

The book concludes that
(s - t)/(t - r) = (x + 2x)/x, which of course is 3.

I do not understand the logic here.
Look at at a simple number line.

4. ## Re: Number Line With r, s, and t

Originally Posted by Plato
Look at at a simple number line.
Yes that's exactly what I would do, except I would leave off the numbers and just mark equal lengths. Always draw a diagram if you can.

5. ## Re: Number Line With r, s, and t

Thank you everyone.