A Level Maths Question - Proportion

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SenpaiMicro
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#1
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#1
Hello,

I have gotten my account back after I lost my password. I have just received a question on proportion (attached below).

The question does not specify how long the walls are or how many workers there are in total, however I assumed that there are only 2. These are the answers I got:

a) t=6n
b) 2 Workers
c) 20 days.
d) 20 workers
e)The south and West wall

I am not sure if these answers are correct, as I could not use the equation worked out in part a as there is a possibility that the walls are not the same length.

Thanks!
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mqb2766
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#2
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#2
(Original post by SenpaiMicro)
Hello,

I have gotten my account back after I lost my password. I have just received a question on proportion (attached below).

The question does not specify how long the walls are or how many workers there are in total, however I assumed that there are only 2. These are the answers I got:

a) t=6n
b) 2 Workers
c) 20 days.
d) 20 workers
e)The south and West wall

I am not sure if these answers are correct, as I could not use the equation worked out in part a as there is a possibility that the walls are not the same length.

Thanks!
As its rectangular, how can the south and west be the shortest?
As usual, upload your working if you want it checked.
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Muttley79
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#3
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#3
(Original post by SenpaiMicro)
Hello,

I have gotten my account back after I lost my password. I have just received a question on proportion (attached below).

The question does not specify how long the walls are or how many workers there are in total, however I assumed that there are only 2. These are the answers I got:

a) t=6n
b) 2 Workers
c) 20 days.
d) 20 workers
e)The south and West wall

I am not sure if these answers are correct, as I could not use the equation worked out in part a as there is a possibility that the walls are not the same length.

Thanks!
We are told its rectangular ...

I don't agree with a) if n = 1 the wall takes less time ie 6 days
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SenpaiMicro
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#4
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(Original post by Muttley79)
We are told its rectangular ...

I don't agree with a) if n = 1 the wall takes less time ie 6 days
Oh yeah I forgot, so is the equation t=k/n? Then I work out the constant from there?
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SenpaiMicro
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#5
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(Original post by mqb2766)
As its rectangular, how can the south and west be the shortest?
As usual, upload your working if you want it checked.
My working was:
Total time = 50 days.
Time taken to build the north wall and South wall = 12+8 = 20
50-20 = 30 days
Time taken to build East and West wall = 30 days
Time taken to build East wall = 2*time taken to build the west wall

E = 2W

2W + W = 30
3W = 30
W = 10
Therefore time taken to build the east wall is 20 days.
The south took the least time (8 days) and the west took 10 days. I am not sure if this is right but it is how I worked it out.
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mqb2766
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#6
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#6
(Original post by SenpaiMicro)
My working was:
Total time = 50 days.
Time taken to build the north wall and South wall = 12+8 = 20
50-20 = 30 days
Time taken to build East and West wall = 30 days
Time taken to build East wall = 2*time taken to build the west wall

E = 2W

2W + W = 30
3W = 30
W = 10
Therefore time taken to build the east wall is 20 days.
The south took the least time (8 days) and the west took 10 days. I am not sure if this is right but it is how I worked it out.
Those times sound about right. So what about the other question parts.
Its easier if you state which question part you're answering when you post work.

Note, Im presuming this isnt the answer to e).
Last edited by mqb2766; 3 months ago
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SenpaiMicro
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#7
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#7
(Original post by mqb2766)
Those times sound about right. So what about the other question parts.
Its easier if you state which question part you're answering when you post work.

Note, Im presuming this isnt the answer to e).
I am stuck on b and d as I am unsure how many workers are present and I am wondering if my answers are right.
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mqb2766
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#8
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#8
(Original post by SenpaiMicro)
I am stuck on b and d as I am unsure how many workers are present and I am wondering if my answers are right.
Your times for the different walls seem right.
What did you get for a) and how will it relate to b)?

Note a sketch of the problem and annotating with num of people, times, ... would probably help.
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SenpaiMicro
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#9
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#9
(Original post by mqb2766)
Your times for the different walls seem right.
What did you get for a) and how will it relate to b)?

Note a sketch of the problem and annotating with num of people, times, ... would probably help.
I was thinking that the expression for the time taken for each of the walls would be different as the lengths of the walls may be different to that of the North wall so I was thinking the constant of 6 would only apply to the North wall and therefore I cant use it for any of the other walls. Am I able to use this constant for the other walls despite the difference in length?
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mqb2766
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#10
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#10
(Original post by SenpaiMicro)
I was thinking that the expression for the time taken for each of the walls would be different as the lengths of the walls may be different to that of the North wall so I was thinking the constant of 6 would only apply to the North wall and therefore I cant use it for any of the other walls. Am I able to use this constant for the other walls despite the difference in length?
Firstly, its a rectangle so ....
Also think about what the constant represents and how you calculate it.

Drawing a sketch as per the previous post with information marked on is recommended.
Last edited by mqb2766; 3 months ago
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SenpaiMicro
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#11
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(Original post by mqb2766)
Firstly, its a rectangle so ....
Also think about what the constant represents and how you calculate it.

Drawing a sketch as per the previous post with information marked on
Alright so I have fully solved the question I will present my working below:

a) the time taken to build the wall is inversely proportional to the number of builders.

Therefore, t = k/n

The time taken to build the north wall using 2 builders was 12 days therefore the constant is:

12=k/2
k=24
Therefore the relationship between the number of workers and the time taken is represented as t=24/n

b) It took 8 days to finish the south fence therefore using the equation above we can work out the number of workers as:

8 = 24/n
8n=24
n = 3 (3 workers).

c)

Total time = 50 days.
Time taken to build the north wall and South wall = 12+8 = 20
50-20 = 30 days
Time taken to build East and West wall = 30 days
Time taken to build East wall = 2*time taken to build the west wall

E = 2W

2W + W = 30
3W = 30
W = 10

Therefore the time taken to build the east wall was 20 days.

d) Using the diagram of a rectangle we can see that the length of the west and the east fence are the same. It is stated that it took twice as much time to finish the east than the west wall. Therefore with the workers working at the same rate it must be that there was half as many workers working on the east wall than the west wall therefore 4 builders worked on the west wall.

e) The fences increase in size going from smallest to largest listed below:
South (and North), and west (and East).

Is this correct?
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mqb2766
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#12
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#12
Agree with that, though e) only asks for the shortest walls.
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SenpaiMicro
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#13
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#13
(Original post by mqb2766)
Agree with that, though e) only asks for the shortest walls.
Oh yeah I forgot about that, thank you very much for helping me! I appreciate it very much
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