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AQA GCSE · Question 15.2 · Ratio Proportion and Rates of Change
After the bath is full, the volume of water stays constant for 20 minutes, then all the water empties out at a constant rate in 12 minutes. Complete the graph to show this information.
After the bath is full, the volume of water stays constant for 20 minutes, then all the water empties out at a constant rate in 12 minutes. Complete the graph to show this information.
How to approach this question
1. The bath is full at 10 minutes with a volume of 240 litres. This is the point (10, 240).
2. The volume stays constant for 20 minutes. This means for the next 20 minutes, the volume remains at 240 litres. The time will be 10 + 20 = 30 minutes. So, draw a horizontal line from (10, 240) to (30, 240).
3. The water then empties in 12 minutes. This starts at time t=30 minutes. It will be empty at t = 30 + 12 = 42 minutes.
4. "Empty" means the volume is 0 litres. So, the line must go from the point (30, 240) down to the point (42, 0).
5. Draw a straight line connecting these two points.
Full Answer
The completed graph should show:
1. A horizontal line from (10, 240) to (30, 240).
2. A straight line from (30, 240) down to (42, 0).
The question asks to add two more stages to the graph.
Stage 2: Water stays constant for 20 minutes.
- The bath is full at t=10 minutes, with a volume of 240 litres.
- The volume stays at 240 litres for the next 20 minutes.
- This stage ends at t = 10 + 20 = 30 minutes.
- On the graph, this is a horizontal line from the point (10, 240) to the point (30, 240).
Stage 3: Water empties in 12 minutes.
- This stage starts at t=30 minutes, when the volume is 240 litres.
- It takes 12 minutes to empty, so it will be empty at t = 30 + 12 = 42 minutes.
- "Empty" means the volume is 0 litres.
- On the graph, this is a straight line from the point (30, 240) down to the point (42, 0).
The final graph will have three line segments:
1. From (0, 0) to (10, 240).
2. From (10, 240) to (30, 240).
3. From (30, 240) to (42, 0).
Common mistakes
✗ Drawing the horizontal line for 20 minutes starting from t=0 instead of t=10.
✗ Calculating the end time for emptying incorrectly (e.g., ending at t=12 instead of t=42).
✗ Drawing a curve instead of a straight line for the emptying phase.
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