A cyclist travels from point A to point B, a distance of 12 km, in 30 minutes. They then stop at point B for 1.5 hours before cycling to point C, 20 km from A, in another 30 minutes. Draw a distance-t

a) To draw the distance-time graph for the cyclist:

Step 1: Determine the coordinates for each segment of the journey.

• Segment 1: From A to B

  • Start time: 6:30 am
  • End time: 7:00 am
  • Duration: $7:00 \text{ am} - 6:30 \text{ am} = 30 \text{ minutes}$
  • Distance covered: 12 km
  • Point 1: $(6:30 \text{ am}, 0 \text{ km})$
  • Point 2: $(7:00 \text{ am}, 12 \text{ km})$

• Segment 2: Stop at B

  • Start time: 7:00 am
  • Duration of stop: $1\frac{1}{2} \text{ hours} = 1 \text{ hour } 30 \text{ minutes}$
  • End time of stop: $7:00 \text{ am} + 1 \text{ hour } 30 \text{ minutes} = 8:30 \text{ am}$
  • Distance covered: 0 km (distance remains 12 km)
  • Point 3: $(8:30 \text{ am}, 12 \text{ km})$

• Segment 3: From B to C

  • Start time: 8:30 am
  • Starting distance: 12 km
  • Destination C is 20 km away.
  • Distance to cover: $20 \text{ km} - 12 \text{ km} = 8 \text{ km}$
  • Speed: 16 km/h
  • Time taken: $\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{8 \text{ km}}{16 \text{ km/h}} = 0.5 \text{ hours} = 30 \text{ minutes}$
  • End time: $8:30 \text{ am} + 30 \text{ minutes} = 9:00 \text{ am}$
  • End distance: 20 km
  • Point 4: $(9:00 \text{ am}, 20 \text{ km})$

Step 2: Set up the graph axes according to the given scale.

• Vertical axis (Distance): 2 cm represents 4 km. If each grid square is 1 cm, then 2 squares represent 4 km. Label the axis from 0 km to 20 km (e.g., 0, 4, 8, 12, 16, 20).
• Horizontal axis (Time): 2 cm represents 30 minutes. If each grid square is 1 cm, then 2 squares represent 30 minutes. Label the axis starting from 6:30 am (e.g., 6:30 am, 7:00 am, 7:30 am, 8:00 am, 8:30 am, 9:00 am).

Step 3: Plot the points and draw the graph.

1. Plot the starting point: $(6:30 \text{ am}, 0 \text{ km})$.
2. Draw a straight line from $(6:30 \text{ am}, 0 \text{ km})$ to $(7:00 \text{ am}, 12 \text{ km})$.
3. Draw a horizontal line from $(7:00 \text{ am}, 12 \text{ km})$ to $(8:30 \text{ am}, 12 \text{ km})$ to represent the stop.
4. Draw a straight line from $(8:30 \text{ am}, 12 \text{ km})$ to $(9:00 \text{ am}, 20 \text{ km})$.

b) To find the time taken for the cyclist to reach the destination using the graph:

Step 1: Locate the destination distance on the vertical axis.
The destination is 20 km. Find 20 km on the vertical axis.

Step 2: Read the corresponding time on the horizontal axis.
Follow horizontally from 20 km to the graph line, then vertically down to the time axis. This point corresponds to 9:00 am.

Step 3: Calculate the total time taken.
The journey started at 6:30 am and ended at 9:00 am.

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