Poppy and Ella ran a 5 km race - Junior Cycle Mathematics - Question 6 - 2019
Question 6
Poppy and Ella ran a 5 km race. The simplified graph below shows the time that it took Ella to run d km during the race. One of the points on the graph is marked A.
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Worked Solution & Example Answer:Poppy and Ella ran a 5 km race - Junior Cycle Mathematics - Question 6 - 2019
Step 1
Using the figures in the diagram above, draw a graph on the diagram to show the time it took Poppy to run d km during the race, for 0 ≤ d ≤ 5 and d ∈ ℝ.
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Answer
To draw the graph for Poppy, observe that her running time is consistently greater than Ella's. For distances of:
1 km, time = 5 minutes
2 km, time = 10 minutes
3 km, time = 17 minutes
4 km, time = 30 minutes
5 km, time = 26 minutes
Plot points accordingly on the same diagram, ensuring the lines do not intersect as Poppy takes longer than Ella at most distance marks.
Step 2
Using Ella's graph, fill in the three missing values in the table below.
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Answer
Distance in the race (km)
Total time taken for Poppy (minutes)
Total time taken for Ella (minutes)
1
5
4
2
10
14
3
17
20
4
30
24
5
30
26
Step 3
Show that Poppy's times in the table do not make a quadratic sequence.
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Answer
To determine whether Poppy's times form a quadratic sequence, calculate the first differences:
10 - 5 = 5
17 - 10 = 7
30 - 17 = 13
30 - 30 = 0
The first differences are not constant, indicating that the sequence is not quadratic.
Step 4
It took Ella 26 minutes to run the 5 km. Work out Ella's average speed for the race. Give your answer in km per hour, correct to two decimal places.
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Answer
To find Ella's average speed, use the formula:
extSpeed=TimeDistance
Substituting the known values:
Speed=26 min5 km×1 hour60 min=11.54 km/h
Step 5
Tick (✓) the correct box to show what happened Ella's speed after 2 km, which is marked A on the graph. Tick one box only. Justify your answer.
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Answer
Ella's speed decreased. The justification for this can be inferred from the graph where the slope of Ella's line becomes less steep after the 2 km mark, indicating a reduction in speed.
Step 6
What does the part C tell us about Ciarán’s running at this stage of the race? Give as much detail as possible.
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Answer
Part C of Ciarán's graph, which is a vertical line, indicates that he stopped running. This means that for a certain distance, his total time taken continued to increase without any distance being covered, suggesting a pause or a break in running.
Step 7
Give a reason why Brendan is correct.
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Brendan is correct because a function must have one output for each input. In Ciarán’s graph, the vertical line implies multiple times for the same distance, which violates the definition of a function.
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