Math Problem Statement

Calculate the mean walking speed of all the students. Tick ( ) one box.

[1]

A. 1.5 m/s

B. 11.9 m/s

C. 1.7 m/s

(c) Choose the median walking speed of all the students. Tick ( ) one box.

[1]

A. 1.7 m/s

B. 1.5 m/s

C. 0.6 m/s

  1. The distance-time graph below shows the movement of three objects A, B
Calculate the mean walking speed of all the students. Tick ( ) one box. A. 1.5 m/s B. 11.9 m/s C. 1.7 m/s (c) Choose the median walking speed of all the students. Tick ( ) one box. A. 1.7 m/s B. 1.5 m/s C. 0.6 m/s The distance-time graph below shows the movement of three objects A, B, and C.

Solution

Let's analyze the graph step by step:

1. Understanding the Problem

The graph shows distance (m) versus time (s) for three objects labeled A, B, and C. To find the mean and median walking speeds, we calculate the speed of each object and then determine the mean and median.

2. Calculating Speeds

The speed is given by the formula:

Speed=DistanceTime\text{Speed} = \frac{\text{Distance}}{\text{Time}}

From the graph:

  • Object A reaches 100 m in 2 seconds.
  • Object B reaches 100 m in 5 seconds.
  • Object C reaches 100 m in 10 seconds.

Using the formula:

  • Speed of A:
    vA=100m2s=50m/sv_A = \frac{100 \, \text{m}}{2 \, \text{s}} = 50 \, \text{m/s}

  • Speed of B:
    vB=100m5s=20m/sv_B = \frac{100 \, \text{m}}{5 \, \text{s}} = 20 \, \text{m/s}

  • Speed of C:
    vC=100m10s=10m/sv_C = \frac{100 \, \text{m}}{10 \, \text{s}} = 10 \, \text{m/s}

3. Mean Walking Speed

The mean walking speed is the average of the three speeds:

Mean Speed=Sum of SpeedsNumber of Objects\text{Mean Speed} = \frac{\text{Sum of Speeds}}{\text{Number of Objects}}

Substitute values:

Mean Speed=50+20+103=80326.7m/s\text{Mean Speed} = \frac{50 + 20 + 10}{3} = \frac{80}{3} \approx 26.7 \, \text{m/s}

None of the options match the high-speed values. Please confirm if this is the question intended, as 50 m/s for walking seems unusually fast. Otherwise, clarify or request adjustments!

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Math Problem Analysis

Mathematical Concepts

Speed Calculation
Mean and Median
Distance-Time Graph

Formulas

Speed = Distance / Time
Mean = (Sum of Values) / (Number of Values)
Median = Middle Value of an Ordered Dataset

Theorems

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Suitable Grade Level

Grades 6-8