Question

1. tamara either runs or walks the same route each day. last month, she ran half of the days and walked the other days. which graph best represents the distance she traveled each day? a. graph with distance on y - axis, time on x - axis, horizontal line b. graph with distance on y - axis, time on x - axis, line from (0,0) with constant slope c. graph with distance on y - axis, time on x - axis, two segments: steeper then less steep d. graph with distance on y - axis, time on x - axis, triangle: distance increases then decreases © gina wilson (all things algebra®, llc), 2012 - 2018

Explanation:

Step1: Analyze the motion types

Tamara runs or walks the same route. Running speed \( v_{run} \) is greater than walking speed \( v_{walk} \). Distance \( d = v\times t \), so for the same distance, time \( t=\frac{d}{v} \), meaning running takes less time than walking for the same distance.

Step2: Analyze each graph

• Graph A: Distance is constant with time, which would mean no motion (speed = 0), incorrect.
• Graph B: A single linear line, implying constant speed (same motion type), but she has two motion types (run/walk), incorrect.
• Graph C: Two linear segments. The first segment (steeper) represents higher speed (running, less time for same distance), the second (less steep) represents lower speed (walking, more time for same distance). This matches her running half the days (higher speed, steeper slope) and walking the other days (lower speed, less steep slope) for the same route (same distance).
• Graph D: A triangular graph, implying distance first increases then decreases (like going and coming back), but she travels the same route (one - way, distance should not decrease), incorrect.

Answer:

C