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AQA GCSE · Question 10 · Ratio Proportion and Rates of Change
A car will travel 60 miles. Draw a graph to show the average speed of the car for times taken between 1 hour and 6 hours. You may use the table to help you.
A car will travel 60 miles. Draw a graph to show the average speed of the car for times taken between 1 hour and 6 hours. You may use the table to help you.
How to approach this question
1. Understand the relationship between speed, distance, and time: Speed = Distance / Time.
2. The distance is constant at 60 miles. The time taken varies from 1 to 6 hours.
3. Use the formula to calculate the average speed for each time value in the table (t=3, 4, 5).
4. For example, when time = 3 hours, speed = 60 / 3 = 20 mph.
5. Once the table is complete, you will have a set of coordinate pairs (Time, Speed).
6. Plot these points on the provided axes.
7. Connect the points with a smooth curve, not straight lines.
Full Answer
First, complete the table using the formula: Average Speed = Distance / Time. The distance is fixed at 60 miles.
- Time = 1 hour: Speed = 60/1 = 60 mph
- Time = 2 hours: Speed = 60/2 = 30 mph
- Time = 3 hours: Speed = 60/3 = 20 mph
- Time = 4 hours: Speed = 60/4 = 15 mph
- Time = 5 hours: Speed = 60/5 = 12 mph
- Time = 6 hours: Speed = 60/6 = 10 mph
Then, plot these points on the graph: (1, 60), (2, 30), (3, 20), (4, 15), (5, 12), (6, 10).
Finally, draw a smooth curve connecting these points.
The relationship between average speed (S), distance (D), and time (T) is given by the formula S = D/T.
In this problem, the distance is fixed at D = 60 miles. So the formula is S = 60/T. This is an inverse proportion relationship, which will produce a curve on the graph.
First, we complete the table by calculating the speed for each given time:
- When T = 1, S = 60/1 = 60 mph.
- When T = 2, S = 60/2 = 30 mph.
- When T = 3, S = 60/3 = 20 mph.
- When T = 4, S = 60/4 = 15 mph.
- When T = 5, S = 60/5 = 12 mph.
- When T = 6, S = 60/6 = 10 mph.
Next, we plot these coordinate pairs (T, S) on the graph:
(1, 60), (2, 30), (3, 20), (4, 15), (5, 12), (6, 10).
Finally, we connect these points with a smooth curve. The graph should start high on the left and curve downwards to the right, getting flatter as time increases.
Common mistakes
✗ Joining the points with straight lines instead of a smooth curve.
✗ Incorrectly calculating the speed values.
✗ Plotting the points inaccurately on the graph, for example misinterpreting the scale on the y-axis.
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