Euros. QUESTION 3: A cabling company has a team of 24 workers who are expected to dig trenches, in order to lay down cables. The team of 24 workers can dig a standard trench in 1 hour. 3.1: Construct a table to show the relationship between the number of workers and the time taken to dig a standard trench. 3.2: What kind of relationship is illustrated in this example? Motivate your answer. 3.3: Use your table from QUESTION 3.1 to: 3.3.1: Determine a formula to represent the time it takes workers to dig a standard trench. 3.3.2: Draw a graph on the attached set of axes of the time it takes the workers to dig a standard trench.

Let's break down the problem step by step. ### 3.1: Constructing the Table We know that 24 workers can dig a standard trench in 1 hour. If we increase or decrease the number of workers, the time taken will change inversely. To create the table, we can calculate the time taken for different numbers of workers. The relationship can be expressed as: \[ \text{Time} = \frac{\text{Standard Time}}{\text{Number of Workers}} = \frac{1 \text{ hour}}{N} \] Where \( N \) is the number of workers. Let's create a table for different values of \( N \): | Number of Workers (N) | Time Taken (hours) | |-----------------------|---------------------| | 1 | 24 | | 2 | 12 | | 3 | 8 | | 4 | 6 | | 6 | 4 | | 8 | 3 | | 12 | 2 | | 24 | 1 | ### 3.2: Type of Relationship The relationship illustrated in this example is an **inverse relationship**. This means that as the number of workers increases, the time taken to dig the trench decreases. The product of the number of workers and the time taken remains constant (in this case, 24 worker-hours). ### 3.3: Formula and Graph #### 3.3.1: Determining the Formula From the table, we can see that the time taken \( T \) in hours can be represented as: \[ T = \frac{24}{N} \] Where \( T \) is the time taken in hours and \( N \) is the number of workers. #### 3.3.2: Drawing the Graph To draw the graph, we will plot the number of workers \( N \) on the x-axis and the time taken \( T \) on the y-axis. The points from the table will be: - (1, 24) - (2, 12) - (3, 8) - (4, 6) - (6, 4) - (8, 3) - (12, 2) - (24, 1) Now, I will create the graph based on these points. Let's proceed to plot the graph. ### Graph Plotting I will now create the graph using the points derived from the table. (Note: Since I cannot create visual graphs directly, I will describe how to plot it.) 1. **X-axis**: Number of Workers (N) 2. **Y-axis**: Time Taken (T) 3. **Plot the points**: Use the points from the table. 4. **Connect the points**: Draw a smooth curve that reflects the inverse relationship. The graph will show a downward curve, indicating that as the number of workers increases, the time taken decreases. If you need a specific graphing tool or software to visualize this, please let me know!