Facts: The graph refers to a plane's flight from one location to another. The vertical axis represents the distance, in...

Owning the Dataset

Table 1: Text Analysis

Table 2: Chart Analysis

Key Insights

1. The plane's distance from its destination mostly decreases, aligning with a typical flight trajectory.
2. There is one unusual period (60–80 minutes) where the plane briefly increases its distance from the destination, suggesting an anomaly such as diversion or holding pattern.
3. The flight's fastest progress toward the destination happens between 180 and 200 minutes, seen in the steepest drop in distance on the graph.

Step-by-Step Solution

Question 1: Comparison of Plane's Proximity to Destination at Two Times

Complete Statement:

The plane was closer to its destination at [BLANK 1]

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: closer to its destination
    Meaning: We are being asked to determine at which of two times the plane was physically closer to its final destination.
    Relation to Chart: This is measured by the y-axis value (distance from destination) — the lower the value, the closer the plane is.
    Important Implications: A lower y-axis (distance) value at a given time point means the plane is closer to its destination.

• Statement Breakdown 2:
  • Key Phrase: at [BLANK 1]
    Meaning: We're to choose which pair of times fits this description from among the dropdown options.
    Relation to Chart: For each possible answer, we compare y-values at two different times as shown on the chart.
    Important Implications: Normally, as time progresses, the plane gets closer to its destination, but we're being asked to notice if there is an exception to this trend.

• What is needed: The pair of times for which the earlier time showed the plane actually closer to its destination than the later time.

Solution:

• Condensed Solution Implementation:
  Survey the chart for all given pairs of times. For each, compare the y-values (distances). Usually, the later time is closer, but we check carefully for any anomaly.
• Necessary Data points:
  Identify the y-values (distances from destination) at t = 60 and t = 80. At t = 60, the distance is about 190 km; at t = 80, the distance increases to about 200 km.
  Calculations Estimations:
  Since 190 km (at t = 60) < 200 km (at t = 80), the plane was closer at t = 60 than at t = 80. All other pairs follow the normal trend: the later time is closer.
  Comparison to Answer Choices:
  The only time pair matching the condition is 't = 60 than at t = 80'. This is the anomaly; all other options are not exceptions.

FINAL ANSWER Blank 1: t = 60 than at t = 80

Question 2: Greatest Progress Toward Destination in a 20-Minute Interval

Complete Statement:

Of all of the 20-minute intervals beginning and ending at times labeled on the graph, the interval in which the plane traveled farthest toward its destination was the interval from [BLANK 2]

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: 20-minute intervals beginning and ending at times labeled on the graph
    Meaning: We're limited to intervals of exactly 20 minutes, starting and ending at times printed on the chart's x-axis.
    Relation to Chart: We are to analyze the slope (drop) of the distance in each of those intervals.

• Statement Breakdown 2:
  • Key Phrase: traveled farthest toward its destination
    Meaning: We need to identify where the plane made the largest decrease in distance within one interval.
    Relation to Chart: Look for the interval with the steepest downward slope on the graph.

• What is needed: Which 20-minute interval saw the largest drop (decrease) in distance to the destination.

Solution:

• Condensed Solution Implementation:
  Visually check each eligible 20-minute interval on the graph and measure the change in distance (how much the y-value decreases).
• Necessary Data points:
  For t = 180 to t = 200, the distance drops from about 120 km to about 60 km, a change of about 60 km downward. Other intervals either have a smaller downward change or, in the case of t = 60 to t = 80, even an increase.
  Calculations Estimations:
  60 km reduction over the interval t = 180 to t = 200 is the largest downward movement among the options.
  Comparison to Answer Choices:
  No other 20-minute interval has as large a decrease. Thus, t = 180 to t = 200 is the answer.

FINAL ANSWER Blank 2: t = 180 to t = 200

Summary

To answer both questions, carefully read the graph. Question 1 required noticing the unusual increase in distance between t = 60 and t = 80, so the earlier time (t = 60) was closer. Question 2 is solved by finding the steepest drop in any 20-minute interval, which occurs from t = 180 to t = 200.

Question Independence Analysis

The two questions are independent. Question 1 asks about a detail in one time pair, while Question 2 looks for the greatest change over an interval. You can answer each without knowledge of the other.