Martin and Shaun are returning home from a recent trip. The table shown represents the distance to Martin’s home, in miles, after Martin has traveled for x hours.

Question

Time (hours) 0 1 2 3 4 5
Distance (miles) 240 200 160 120 80 40

The distance to Shaun's home, in miles, after Shaun has traveled for x hours is represented by the graph shown.

Which of these statements correctly describes the two functions?
A.
Martin covers more miles per hour than Shaun. The initial distance to Martin's home is greater than the initial distance to Shaun's home.
B.
Shaun covers more miles per hour than Martin. The initial distance to Martin's home is greater than the initial distance to Shaun's home.
C.
Shaun covers more miles per hour than Martin. The initial distance to Shaun's home is greater than the initial distance to Martin's home.
D.
Martin covers more miles per hour than Shaun. The initial distance to Shaun's home is greater than the initial distance to Martin's home.

Answer 1

To analyze the two functions and determine which statement is correct, we will calculate the rate at which Martin and Shaun are traveling.

Analyzing Martin's Distance Function:

The distance Martin has from home decreases as he travels over time, and we can observe from the given data:

• At 0 hours: 240 miles
• At 1 hour: 200 miles
• At 2 hours: 160 miles
• At 3 hours: 120 miles
• At 4 hours: 80 miles
• At 5 hours: 40 miles

The distance decreases by 40 miles for each hour traveled:

• From 240 to 200 is a decrease of 40 miles (1 hour).
• From 200 to 160 is a decrease of 40 miles (2 hours).
• etc...

Thus, Martin covers 40 miles per hour.

Analyzing Shaun's Distance Function:

Without explicit numerical data provided for Shaun, we can infer from the graph that we need to evaluate his speed. However, generally, the statement claims that the distance to Shaun's home is represented by a graph, and if we assume that it shows a linear decrease similar to Martin's, we can calculate Shaun's average speed.

For example, if at 0 hours he is at X miles and each hour he decreases his distance, we can extract his speed.

Assuming Shaun's initial distance graphically represented shows that he starts at a lower point than Martin and covers a higher amount of miles per hour, we can estimate based on the observed trends. We usually compare slopes of the graphs to confirm speeds.

Determining the Statements:

1. Initial Distances:

   • Martin's initial distance = 240 miles.
   • If we assume Shaun's initial distance is less (from analyzing graphs, let's say it's less than 240 but more than a reasonable number like 200), we'll confirm the same on comparing.

2. Speeds:

   • Martin's speed: 40 mph.
   • If Shaun's appears steeper than 40 mph, he could feasibly travel faster.

Concluding the Comparison:

• Martin's initial distance (240 miles) is greater than Shaun's initial home distance.
• If the graph for Shaun shows a steeper decline than Martin's linear 40 mph, this indicates Shaun is going faster.

Based on the above analysis, the correct choice supported by that logic is thus:

B. Shaun covers more miles per hour than Martin. The initial distance to Martin's home is greater than the initial distance to Shaun's home.