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AQA GCSE · Question 15.1 · Ratio Proportion and Rates of Change
The graph represents the volume of water in a bath. The bath is full after 10 minutes. Work out the rate at which the bath is filled. State the units of your answer.
The graph represents the volume of water in a bath. The bath is full after 10 minutes. Work out the rate at which the bath is filled. State the units of your answer.
How to approach this question
1. The rate is the gradient (steepness) of the line.
2. Gradient = (change in y) / (change in x).
3. From the graph, identify two points on the line. The easiest are (0, 0) and the end point (10, 240).
4. The change in y (Volume) is 240 - 0 = 240 litres.
5. The change in x (Time) is 10 - 0 = 10 minutes.
6. Calculate the rate: Rate = 240 litres / 10 minutes.
7. The rate is 24 litres/minute.
8. State the units, which are litres per minute.
Full Answer
The rate at which the bath is filled is the gradient of the line on the graph.
The gradient is calculated as the "rise" (change in vertical axis) divided by the "run" (change in horizontal axis).
From the graph:
- At time = 0 minutes, the volume is 0 litres.
- At time = 10 minutes, the bath is full, and the volume is 240 litres.
Change in volume (rise) = 240 - 0 = 240 litres.
Change in time (run) = 10 - 0 = 10 minutes.
Rate = Change in volume / Change in time
Rate = 240 litres / 10 minutes
Rate = 24 litres per minute.
The units are taken from the axes labels: litres for the vertical axis and minutes for the horizontal axis.
Common mistakes
✗ Dividing time by volume instead of volume by time (10/240).
✗ Reading the values from the axes incorrectly.
✗ Forgetting to state the units or giving incorrect units.
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