Question

A conductor is mapping a trip and records the distance the train travels over certain time intervals. time (hours) distance (miles) 0.5 22.5 1 45 1.5 67.545 The train travels at a constant speed. What is its speed in miles per hour?

Answer 1

Given:

Table of values.

The train travels at a constant speed.

To find:

The speed of train in miles per hour.

Solution:

From the given table consider any two points, i.e., (0.5,22.5) and (1,45).

The train travels at a constant speed. It means, there is a linear relationship between time and distance.

The average rate of change (Slope) of a linear relationship is

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

$m=\dfrac{45-22.5}{1-0.5}$

$m=\dfrac{22.5}{0.5}$

$m=\dfrac{225}{5}$

$m=45$

So, average rate of change in distance with respect to time is 45.

Therefore, the speed of the train is 45 miles per hour.