The train changes position over time, therefore the train is moving and so the train has speed. Speed is a rate of change. In order to calculate an average speed for the train we need to determine how much distance the train covered $(\Delta f)$ and how much time it took to cover that distance $(\Delta t)\text{.}$ Consider the interval $1.5 \leq t \leq 2.0\text{.}$

1. What is $\Delta f$ on this interval?
   $\Delta f \approx$ ? miles units hours miles per hour .
2. What is $\Delta t$ on this interval?
   $\Delta t =$ ? hours per mile miles hours units .
3. Use the values you just found to calculate $\frac{\Delta f}{\Delta t}\text{.}$
   $\frac{\Delta f}{\Delta t} \approx$ ? hours hours per mile miles per hour miles .
4. What does $\frac{\Delta f}{\Delta t}$ represent in this situation?
   $\frac{\Delta f}{\Delta t}$ represents the ? distance of the train from downtown average speed of the train time train has traveled triangle D over triangle t .
5. Interpret the meaning of the mathematical expression in the context of the train story:
   $\frac{\Delta f}{\Delta t} = 45$ on the interval $2 \leq t \leq 5$ means the ? distance of the train from downtown time the train has traveled average speed of the train triangle D divided by triangle t is ? miles hours per mile hours miles per hour between ? 2 p.m. and 5 p.m. 10 a.m. and 1 p.m. 2 and 5 2 mph and 5 mph .