One day we decided to drive from Town A to Town D. In order to get there we had to drive through Town B and then Town C. It is 10 miles farther from Town A to Town B than it is from Town B to C. IT is 10 miles farther from Town B to Town C than it is from Town C to Town D. It is 330 miles from Town A to Town D. How far is it from Town A to Town B?

let the distance from c --> d be x

if b --> c is ten miles farther than x, then let that distance be x+10
same for a --> b. it is 10 further than
b --> c (x+10), so it would be x+10+10, or x+20
so look at it like so:
a --x+20->b--x+10->c--x->d
the total distance is (x+20)+(x+10)+x = 330, or 3x+30=330
-30 -30
3x=300
divede by 3, and x=100 miles.
to get a->b, u do 100+20=120 miles

the -30 -30 was subtract 30 from both sides. it lined up in the box but not when posted -_-

To solve this problem, let's break it down step by step and determine the distances between each town.

Let's assume the distance from Town A to Town B is represented by the variable 'x'.

According to the given information, it is 10 miles farther from Town A to Town B than it is from Town B to Town C. So the distance from Town B to Town C would be 'x - 10'.

Similarly, it is 10 miles farther from Town B to Town C than it is from Town C to Town D. So the distance from Town C to Town D would be 'x - 10 - 10', which simplifies to 'x - 20'.

Now, if we add up all these distances, we get the total distance from Town A to Town D. According to the problem, this distance is 330 miles, so we can set up the equation:

x + (x - 10) + (x - 20) = 330

Simplifying the equation:

3x - 30 = 330

Adding 30 to both sides:

3x = 360

Dividing both sides by 3:

x = 120

Therefore, the distance from Town A to Town B is 120 miles.