Question

choose the correct answer. a jogger runs 12 miles in 2 hours. \\(\frac{12\text{ mi}}{2\text{ hrs}}\\) which graph describes this ratio? hint: use the unit rate!

Explanation:

Step1: Calculate unit rate

The jogger runs 12 miles in 2 hours. The unit rate (speed) is $\frac{12\ \text{mi}}{2\ \text{hrs}} = 6\ \text{mi/hr}$. This means for every 1 hour, the distance is 6 miles.

Step2: Analyze graphs

• First graph: The slope (rate) seems less than 6 (e.g., at 6 hours, distance is low), so not correct.
• Second graph: Let's check points. At 1 hour, distance should be 6. If the graph has a point (1,6), (2,12), etc., which matches the unit rate of 6 mi/hr. For example, when time $t = 1$, distance $d = 6\times1 = 6$; $t = 2$, $d = 12$, which aligns with the graph's trend.
• Third graph: At 1 hour, distance is 8 (or more), which is more than 6, so incorrect.

Answer:

The Middle Graph