Tina is standing beside a race-track - Junior Cycle Mathematics - Question 9 - 2014
Question 9
Tina is standing beside a race-track. A red car and a blue car are travelling in the same direction at steady speeds on the track. At a particular time the red car h... show full transcript
Worked Solution & Example Answer:Tina is standing beside a race-track - Junior Cycle Mathematics - Question 9 - 2014
Step 1
Complete the table below to show the distance between the red car and the blue car and Tina during the next 9 seconds.
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Answer
To complete the table, we can use the formula for distance:
For the red car:
Distance = 70 + 20t (where t is time in seconds)
For the blue car:
Distance = 20 + 30t (where t is time in seconds)
Calculating distances for each second:
At t = 0: Red car = 70, Blue car = 20
At t = 1: Red car = 90, Blue car = 50
At t = 2: Red car = 110, Blue car = 80
At t = 3: Red car = 130, Blue car = 110
At t = 4: Red car = 150, Blue car = 140
At t = 5: Red car = 170, Blue car = 170
At t = 6: Red car = 190, Blue car = 200
At t = 7: Red car = 210, Blue car = 230
At t = 8: Red car = 230, Blue car = 260
At t = 9: Red car = 270, Blue car = 290
Step 2
After how many seconds will both cars be the same distance from Tina?
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Answer
Both cars will be the same distance from Tina after 5 seconds, as calculated in the previous table where both distances are equal at 170 m.
Step 3
After 8 seconds which car is furthest from Tina and how far ahead of the other car is it?
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Answer
After 8 seconds, the distances are:
Red Car = 230 m
Blue Car = 260 m
Thus, the blue car is furthest from Tina by 30 m.
Step 4
On the diagram below draw graphs of the distance between the red car and Tina and the distance between the blue car and Tina over the 9 seconds.
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Answer
For this part, the graph should show two lines:
The red car distance starts at 70 m and increases steadily to 270 m.
The blue car distance starts at 20 m and increases steadily to 290 m.
The x-axis is time (0 to 9 seconds) and the y-axis is distance (0 to 300 m).
Step 5
Write down a formula to represent the distance between the red car and Tina for any given time.
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Answer
The formula for the distance between the red car and Tina is:
Distance = 70 + 20t
Where t is the time in seconds.
Step 6
Write down a formula to represent the distance between the blue car and Tina for any given time.
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Answer
The formula for the distance between the blue car and Tina is:
Distance = 20 + 30t
Where t is the time in seconds.
Step 7
Use your formulas from (v) and (vi) to verify the answer that you gave to part (ii) above.
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Answer
Let the distance from (v) and (vi) equal:
70 + 20t = 20 + 30t
Solving gives:
70 - 20 = 30t - 20t
50 = 10t
5 = t
Thus, both cars are the same distance from Tina after 5 seconds.
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