The problem describes Priya jogging at a constant speed, represented by the given graph, and Diego biking at twice Priya's speed. We need to analyze the graph and sketch the relationship between Diego's distance and time.

Analysis:

1. The graph shows that Priya's distance increases linearly with time, which means she is jogging at a constant speed. From the graph, it appears that Priya jogs 2 miles in 0.5 hours, which gives her speed: $\text{Speed of Priya} = \frac{\text{Distance}}{\text{Time}} = \frac{2 \, \text{miles}}{0.5 \, \text{hours}} = 4 \, \text{miles per hour}.$

2. Diego's speed is twice Priya's speed: $\text{Speed of Diego} = 2 \times 4 \, \text{miles per hour} = 8 \, \text{miles per hour}.$

3. Since speed is the slope of the distance-time graph, Diego’s graph will also be linear but with a slope twice that of Priya's graph.

Sketching Diego's Graph:

To represent Diego's distance on the graph:

• At $t = 0$, Diego’s distance is $0$ miles (just like Priya).
• At $t = 0.5 \, \text{hours}$, Diego travels: $\text{Distance} = \text{Speed} \times \text{Time} = 8 \times 0.5 = 4 \, \text{miles}.$
• At $t = 1 \, \text{hour}$, Diego travels: $\text{Distance} = 8 \times 1 = 8 \, \text{miles}.$

The graph for Diego will be a straight line passing through the origin but steeper than Priya's, with a slope of $8$ miles per hour.

Would you like a sketch of Diego's graph? Let me know if you'd like further clarifications.

5 Related Questions:

1. What would be the graph if Diego biked three times as fast as Priya?
2. How does the slope of the line relate to speed in a distance-time graph?
3. If Priya jogged for 2 hours, how far would she travel?
4. How much farther would Diego travel than Priya after 1 hour?
5. What is the mathematical equation of Diego’s distance-time relationship?

Tip:

Always check the slope of a graph to understand the rate of change for real-world problems!