Question

Person A and Person B start walking from the same initial position in different directions. What is the difference in their rate of walking in miles per hour based on the given graph?

• A. $\frac{25}{46}\text{mi per h}$
• B. $\frac{25}{36}\text{mi per h}$
• C. $\frac{5}{36}\text{mi per h}$
• D. $\frac{25}{76}\text{mi per h}$

Answer 1

The correct option is B $\frac{25}{36}\text{mi per h}$

For Person A:
Let’s consider the points (2.25, 1.25) and (0, 0).
Unit rate = slope $=\frac{\text{change in y}}{\text{change in x}}=\frac{1.25-0}{2.25-0}=\frac{5}{9}\text{mi per h}$
For Person B:
On a graph of a proportional relationship, point (1, k) represents the unit rate, k:1, and the constant of proportionality k.
So, from the point (1, 1.25), the unit rate which is the rate of walking here is determined as 1.25 mi per h.
1.25 mi per $h=\frac{5}{4}\text{mi per h}.$
Difference in their rate of walking $=\frac{5}{4}-\frac{5}{9}=\frac{45-20}{36}=\frac{25}{36}\text{mi per h}$