Question 1199939
**1. Determine the Distances Traveled**

* **Cliff:** Since Cliff started 1 hour earlier and walks at 3 kph, he has traveled 3 km east by 9:00 AM.
* **Renz:** Let 't' be the time in hours since 9:00 AM. Renz travels 4t kilometers north.

**2. Use Pythagorean Theorem**

* The distance between Cliff and Renz at time 't' can be found using the Pythagorean theorem:

   d(t) = √[(Cliff's distance)² + (Renz's distance)²] 
   d(t) = √[(3 + 3t)² + (4t)²] 
   d(t) = √(9 + 18t + 9t² + 16t²) 
   d(t) = √(25t² + 18t + 9)

**3. Compare with the Given Expression**

* Compare the derived expression with the given expression: 
    * d(t) = √(at² + 2βt + β) 
    * d(t) = √(25t² + 18t + 9)

* We can see that:
    * a = 25
    * 2β = 18 
        * β = 9

**4. Calculate a - β**

* a - β = 25 - 9 = 16

**Therefore, a - β = 16.**