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 Tina and the blue car and Tina during the next 9 seconds.
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Answer
To calculate the distances for both cars over the next 9 seconds:
For the Red Car:
At time 0s: 70 m
Increases by 20 m for each second:
1s: 90 m
2s: 110 m
3s: 130 m
4s: 150 m
5s: 170 m
6s: 190 m
7s: 210 m
8s: 230 m
9s: 270 m
For the Blue Car:
At time 0s: 20 m
Increases by 30 m for each second:
1s: 50 m
2s: 80 m
3s: 110 m
4s: 140 m
5s: 170 m
6s: 200 m
7s: 230 m
8s: 260 m
9s: 290 m
Step 2
After how many seconds will both cars be the same distance from Tina?
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Answer
To find when both cars are the same distance from Tina, set the distances equal:
Distance of Red Car: 70 + 20t
Distance of Blue Car: 20 + 30t
Set the equations equal:
70+20t=20+30t
Solving for t:
70−20=30t−20t50=10tt=5
Thus, both cars will be at the same distance from Tina after 5 seconds.
Step 3
After 8 seconds which car is furthest away from Tina and how far ahead of the other car is it?
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Answer
After 8 seconds:
Distance of Red Car = 230 m
Distance of Blue Car = 260 m
Thus, the Blue Car is furthest from Tina and is 30 m ahead of the Red Car.
Step 4
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 over time t seconds is:
extDistance=70+20t
Where t is the time in seconds.
Step 5
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 over time t seconds is:
extDistance=20+30t
Where t is the time in seconds.
Step 6
Use your formulas from (v) and (vi) to verify the answer that you gave to part (ii) above.
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Answer
Set the two distance formulas equal:
70+20t=20+30t
Rearranging gives:
70−20=30t−20t50=10tt=5
This confirms that both cars are the same distance from Tina at 5 seconds.
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