Question

Find an equation for the linear model of the situation below and use it to make a prediction.
A train is traveling north at a constant rate. At 3:00 P.M it is 55 miles north of a city. At 4:15 P.M. it is 80 miles north of the city. If d represents the distance in miles, and t represents the time in hours, how many miles north if the city will the train be at 5:45 P.M.?

Answer 1

4:15-3:00=1:15=75min.

80 miles-55 miles=25miles

$$t _ {1} = 3: 0 0 = 1 8 0 \mathrm {m i n}.$$

T=5:45=345 min.

So, speed $= \frac{25\text{miles}}{75\text{min}} = \frac{1\text{miles}}{3\text{min}}$

$$\begin{array}{l} D = 5 5 \text {miles} + (t - t _ {1}) ^ {*} \frac {1 \text {miles}}{3 \text {min}} = 5 5 \text {miles} + (t - t _ {1}) ^ {*} \frac {1 \text {miles}}{3 \text {min}} = \\ = 5 5 \text {miles} + (3 4 5 \text {min.} - 1 8 0 \text {min.}) * \frac {1 \text {miles}}{3 \text {min}} = 5 5 \text {miles} + 1 6 5 \text {min.} \frac {1 \text {miles}}{3 \text {min}} \\ D = 5 5 \text {miles} + 5 5 \text {miles} = 1 1 0 \text {miles} \\ \end{array}$$

Answer:D = 110miles