The time taken to paint a school varies inversely with the number of painters completing the task.
It takes 6 painters a total of 20 days to paint a school.
How many days would it take 15 painters to paint the same school?
- 4.5
- 8
- 15.5
- 50
Algebra, STD2 A4 2022 HSC 24
A student believes that the time it takes for an ice cube to melt (`M` minutes) varies inversely with the room temperature `(T^@ text{C})`. The student observes that at a room temperature of `15^@text{C}` it takes 12 minutes for an ice cube to melt.
- Find the equation relating `M` and `T`. (2 marks)
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- By first completing this table of values, graph the relationship between temperature and time from `T=5^@C` to `T=30^@ text{C}`. (2 marks)
\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \ T\ \ \rule[-1ex]{0pt}{0pt} & \ \ \ 5\ \ \ & \ \ 15\ \ \ & \ \ \ 30\ \ \ \\
\hline
\rule{0pt}{2.5ex} \ \ M\ \ \rule[-1ex]{0pt}{0pt} & & & \\
\hline
\end{array}
--- 0 WORK AREA LINES (style=lined) ---
Show Answers Only
a. `M prop 1/T \ \ =>\ \ M=k/T`
| `12` | `=k/15` | |
| `k` | `=15 xx 12=180` |
`:.M=180/T`
b.
\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \ T\ \ \rule[-1ex]{0pt}{0pt} & \ \ \ 5\ \ \ & \ \ 15\ \ \ & \ \ 30\ \ \\
\hline
\rule{0pt}{2.5ex} \ \ M\ \ \rule[-1ex]{0pt}{0pt} & 36 & 12 & 6 \\
\hline
\end{array}
Show Worked Solution
| a. | `M` | `prop 1/T` |
| `M` | `=k/T` | |
| `12` | `=k/15` | |
| `k` | `=15 xx 12=180` |
`:.M=180/T`
♦♦ Mean mark part (a) 29%.
b.
\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \ T\ \ \rule[-1ex]{0pt}{0pt} & \ \ \ 5\ \ \ & \ \ 15\ \ \ & \ \ 30\ \ \\
\hline
\rule{0pt}{2.5ex} \ \ M\ \ \rule[-1ex]{0pt}{0pt} & 36 & 12 & 6 \\
\hline
\end{array}
♦ Mean mark (b) 44%.
Algebra, STD2 A4 2021 HSC 13 MC
The time taken to clean a warehouse varies inversely with the number of cleaners employed.
It takes 8 cleaners 60 hours to clean a warehouse.
Working at the same rate, how many hours would it take 10 cleaners to clean the same warehouse.
- 45
- 48
- 62
- 75
Algebra, STD2 A4 EQ-Bank 30
The number of trees that can be planted along the fence line of a paddock varies inversely with the distance between each tree.
There will be 108 trees if the distance between them is 5 metres.
- How many trees can be planted if the distance between them is 6 metres? (2 marks)
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- What is the distance between the trees if 120 trees are planted. (1 mark)
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Algebra, STD2 A4 2018 HSC 29c
When people walk in snow, the depth (`D` cm) of each footprint depends on both the area (`A` cm²) of the shoe sole and the weight of the person. The graph shows the relationship between the area of the shoe sole and the depth of the footprint in snow, for a group of people of the same weight.
- The graph is a hyperbola because `D` is inversely proportional to `A`. The point `P` lies on the hyperbola.
- Find the equation relating `D` and `A`. (2 marks)
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- A man from this group walks in snow and the depth of his footprint is 4 cm.
- Use your equation from part (i) to calculate the area of his shoe sole. (1 mark)
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Algebra, STD2 A4 2007 HSC 15 MC
If pressure `(p)` varies inversely with volume `(V)`, which formula correctly expresses `p` in terms of `V` and `k`, where `k` is a constant?
- `p = k/V`
- `p = V/k`
- `p = kV`
- `p = k + V`
Algebra, STD2 A4 2011 HSC 28a
The air pressure, `P`, in a bubble varies inversely with the volume, `V`, of the bubble.
- Write an equation relating `P`, `V` and `a`, where `a` is a constant. (1 mark)
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- It is known that `P = 3` when `V = 2`.
- By finding the value of the constant, `a`, find the value of `P` when `V = 4`. (2 marks)
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- Sketch a graph to show how `P` varies for different values of `V`.
- Use the horizontal axis to represent volume and the vertical axis to represent air pressure. (2 marks)
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Show Answers Only
a. `P = a/V`
b. `P = 1 1/2`
c.
Show Worked Solution
♦ Mean mark (a) 39%
a. `P prop 1/V\ \ =>\ \ P= a/V`
b. `text(When)\ P=3,\ V=2:`
`3= a/2\ \ =>\ \ a=6`
`text(Find)\ P\ text(when)\ V = 4:`
♦ Mean mark (b) 47%
`P=6/4=3/2`
♦♦ Mean mark (c) 26%
| c. | |
Algebra, STD2 A4 2010 HSC 13 MC
The number of hours that it takes for a block of ice to melt varies inversely with the temperature. At 30°C it takes 8 hours for a block of ice to melt.
How long will it take the same size block of ice to melt at 12°C?
- 3.2 hours
- 20 hours
- 26 hours
- 45 hours