In this problem, we need to solve two tasks related to Janine and Johanna's running rates.

Step 1: Calculate the Distance Traveled in 3 Hours

• Janine’s speed: 5.2 km/hr
• Johanna’s speed: 5.6 km/hr
• Time: 3 hours

For each person:

1. Janine's Distance: $5.2 \, \text{km/hr} \times 3 \, \text{hours} = 15.6 \, \text{km}$
2. Johanna's Distance: $5.6 \, \text{km/hr} \times 3 \, \text{hours} = 16.8 \, \text{km}$

So:

• Janine would travel 15.6 km in 3 hours.
• Johanna would travel 16.8 km in 3 hours.

Step 2: Analyzing Similarities and Differences in Their Running Patterns

To address the question about similarities and differences:

• Similarities: Both runners are maintaining constant speeds (steady rates), so their distance versus time graph would be linear, meaning a straight line for each.
• Differences: The rate of speed differs, with Johanna running slightly faster than Janine. This means Johanna’s line on the graph will have a steeper slope than Janine’s, indicating she covers more distance over the same time period.

Creating a graph:

• On a graph with time on the x-axis and distance on the y-axis, you could plot points for each runner at each hour mark (e.g., at 1 hour, 2 hours, and 3 hours).
• The lines for each runner will start from the origin (0,0) and extend upwards, with Johanna's line being steeper due to her higher speed.

Would you like additional details on any of these calculations or steps?

Here are some questions that expand on the problem:

1. What if they both ran for 5 hours? How far would each travel?
2. How would the graph change if Johanna increased her speed to 6 km/hr?
3. What would be the difference in distance after 2 hours instead of 3?
4. If Janine sped up to match Johanna's speed, how would their patterns compare?
5. How would you describe the relationship between speed and distance in terms of proportionality?

Tip: Remember, when comparing rates on a graph, the steeper the slope, the higher the speed.