Question

1. juro traveled to 3 locations during a workday. juro remained at each location a whole number of hours. the graph shows the relationship between the time, in hours, in his workday and total distance, in kilometers, traveled. which of the following values is closest to the average speed, in kilometers per hour, when juro was traveling?

a. 45
b. 57
c. 60
d. 75

Explanation:

Analyze the graph and identify flat segments

The graph shows total distance in kilometers versus time in hours. Juro traveled to 3 locations and remained at each location for a whole number of hours. Remaining at a location means distance does not change, which corresponds to horizontal (flat) segments on the graph.
Looking at the graph:

• The first flat segment is from \(t = 2\) to \(t = 3\) (duration of 1 hour, at distance 100 km).
• The second flat segment is from \(t = 5\) to \(t = 8\) (duration of 3 hours, at distance 300 km).
• The third flat segment is from \(t = 10\) to \(t = 12\) (duration of 2 hours, at distance 450 km).

Determine total time spent traveling

The total time of the workday shown on the graph is 10 hours of active tracking before the final stay, or we can look at the total time span up to the end of the last stay at \(t = 10\) hours when he reaches the final destination.
Let's calculate the total time spent traveling (excluding the hours he remained at the locations):

• Total elapsed time to reach the final destination of 450 km is \(t = 10\) hours.
• The time spent remaining at the first two locations during this journey:
• At the first location (100 km): from \(t = 2\) to \(t = 3\) is \(3 - 2 = 1\) hour.
• At the second location (300 km): from \(t = 5\) to \(t = 8\) is \(8 - 5 = 3\) hours.
• Total non-traveling time during the journey is \(1 + 3 = 4\) hours.
• Therefore, the actual time spent traveling is:

$$ \text{Traveling Time} = 10 \text{ hours} - 4 \text{ hours} = 6 \text{ hours} $$

Calculate the average traveling speed

The total distance traveled to reach the final destination is 450 km.
Using the average speed formula for when Juro was actually traveling:

$$ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Actual Traveling Time}} = \frac{450 \text{ km}}{6 \text{ hours}} = 75 \text{ km/h} $$

Match with the given options

The calculated average speed of 75 km/h matches option D.

Answer:

• A. 45
• B. 57
• C. 60
• D. 75 (Correct answer)