In the problem provided, $Y$ is a point between $X$ and $Z$, and the segments $XY$, $YZ$, and $XZ$ are given as multiples of $b$ and a specific value, respectively. We have the relationships:

• $XY = 6b$
• $YZ = 8b$
• $XZ = 175$

Given that $XZ$ is the entire distance from $X$ to $Z$, and $Y$ is between $X$ and $Z$, the equation $XZ = XY + YZ$ should hold. Substituting the given values:

$175 = 6b + 8b$

Let's solve this equation to find the value of $b$ and then use it to find $YZ$.The value of $b$ is $\frac{25}{2}$ or 12.5, and the length of segment $YZ$ is 100.

If you have any further questions or need more details, feel free to ask! Here are some related questions you might consider:

1. How does changing the value of $XZ$ affect the values of $b$ and $YZ$?
2. What would be the length of $XY$ based on the calculated value of $b$?
3. If the ratio of $XY$ to $YZ$ changes, how would that impact the value of $b$?
4. What is the significance of $b$ in problems involving segment lengths?
5. Can you create a similar problem using different values and ratios for segment lengths?

Tip: When faced with problems involving segments of lines, setting up an equation based on the total length can simplify finding individual segment lengths.