Question

A train leaves a station in the countryside and travels at a constant speed directly toward itsdestination in the city. After 25 minutes of travel, the train is 325 kilometers from itsdestination. After 70 minutes of travel, the train is 262 kilometers from its destination.Complete the equation that describes the relationship between the distance between the trainand its destination in kilometers, d, and the elapsed time in minutes, t.Write your answer using whole numbers or decimals rounded to the nearest tenth.d =t +

Answer 1

ANSWER:

$d=-1.4d+360$

STEP-BY-STEP EXPLANATION:

In this case, what we must do is calculate the slope of the straight line with the points (25, 325) and (70,262)

We calculate the slope with the following formula.

$m=\frac{y_2-y_1}{x_2-x_1}$

replacing:

$m=\frac{262-325}{70-25}=\frac{-63}{45}=\frac{-7}{5}=-1.4$

For the other value, we can calculate it by means of any of the other two points, knowing that an equation in its slope and y-intercept form is the following

$\begin{gathered} y=mx+b \\ y=325 \\ x=25 \\ m=-1.4 \\ \text{solving b} \\ 325=-1.4\cdot25+b \\ b-35=325 \\ b=325+35 \\ b=360 \end{gathered}$

Therefore, the equation is:

$d=-1.4d+360$