Question: It takes Adi 2 hours to drive from home to her office and 3 hours if she drives 15 mph slower. What is the distance between Adi's house and the office?help me create the x equation
1. **State the problem:**
Adi drives from home to her office in 2 hours at a certain speed. If she drives 15 mph slower, it takes her 3 hours. We need to find the distance between her house and office.
2. **Define variables:**
Let $x$ be Adi's original speed in mph.
3. **Write expressions for distance:**
Distance = speed \times time.
- At original speed: distance = $x \times 2 = 2x$
- At slower speed: speed = $x - 15$, time = 3 hours, so distance = $(x - 15) \times 3 = 3(x - 15)$
4. **Set up the equation:**
Since the distance is the same in both cases,
$$2x = 3(x - 15)$$
This is the equation involving $x$ that models the problem.