# A really confusing maths question

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#1
It's so confusing. I don't even know what topic it is. Could anyone walk me through?

A company has to make a large number of boxes.
The company has 6 machines.
All the machines work at the same rate.
When all the machines are working, they can make all the boxes in 11 days.

Day 1: 3
Day 2: 4
Day 3: 5
All other days: 6

Work out the total number of days taken to make all the boxes.
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1 month ago
#2
Have you missed out a section of the question? What does the “day 1:3” mean?
Is it number of machines working on that day?
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#3
(Original post by GabiAbi84)
Have you missed out a section of the question? What does the “day 1:3” mean?
Is it number of machines working on that day?
On the first day there were 3 machines working. Sorry I forgot to make that clear enough. It was a table so I just typed it out.
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1 month ago
#4
(Original post by UrGrandpap)
It's so confusing. I don't even know what topic it is. Could anyone walk me through?

A company has to make a large number of boxes.
The company has 6 machines.
All the machines work at the same rate.
When all the machines are working, they can make all the boxes in 11 days.

Day 1: 3
Day 2: 4
Day 3: 5
All other days: 6

Work out the total number of days taken to make all the boxes.
I remember doing a similar if not identical question at GCSE, and it's really not difficult once you figure out why the information they've given you is useful.

You know that 11 6 machine days completes all boxes. If I were you, I would think about how many 6 machine days Day 1, 2 and 3 are equivalent to, using the fact that all machines work at the same rate. Hope that helps.
Last edited by Zoqua; 1 month ago
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#5
i'm a little confused. aren't day 2 and 3 equivalent to 4 and 5 machines working?

(Original post by Zoqua)
I remember doing a similar if not identical question at GCSE, and it's really not difficult once you figure out why the information they've given you is useful.

You know that 11 6 machine days completes all boxes. If I were you, I would think about how many 6 machine days Day 1, 2 and 3 are equivalent to, using the fact that all machines work at the same rate. Hope that helps.
i'm a little confused. aren't day 2 and 3 equivalent to 4 and 5 machines working?
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1 month ago
#6
Yes, so add up how many machines were working in those 3 days, how many “full days” is that equivalent to?
1
1 month ago
#7
(Original post by UrGrandpap)
i'm a little confused. aren't day 2 and 3 equivalent to 4 and 5 machines working?

i'm a little confused. aren't day 2 and 3 equivalent to 4 and 5 machines working?
I think you have misinterpreted what I said, so I'll clarify. You know that it takes 11 days for 6 machines to complete the work. You also know that all the machines work at the same rate. Therefore a logical approach to find the remaining number of days (ie how many days is 'all other days'), is to find the number of days with 6 machines working, that Days 1, 2 and 3 are equal to combined together, and then subtract this from 11 to work out how many other days there are (as there are 6 machines working for each of those other days). You then know that the total will be this number plus three (as you have the first three days to think about as well).

If you're wondering how to find out how many 6 machine days Days 1, 2 and 3 are equal to, then a good approach might be to think of it in terms of machine hours. By the rules of this forum I can't give you the answer so sorry I can't be more clear.
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#8
(Original post by GabiAbi84)
Yes, so add up how many machines were working in those 3 days, how many “full days” is that equivalent to?
so um day 3 had 9 machines working?
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1 month ago
#9
(Original post by UrGrandpap)
so um day 3 had 9 machines working?
Not quite. How many days with 6 machines working is a day with 3 machines working equal to, in terms of production?
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#10
(Original post by Zoqua)
Not quite. How many days with 6 machines working is a day with 3 machines working equal to, in terms of production?
(Original post by Zoqua)
I think you have misinterpreted what I said, so I'll clarify. You know that it takes 11 days for 6 machines to complete the work. You also know that all the machines work at the same rate. Therefore a logical approach to find the remaining number of days (ie how many days is 'all other days'), is to find the number of days with 6 machines working, that Days 1, 2 and 3 are equal to combined together, and then subtract this from 11 to work out how many other days there are (as there are 6 machines working for each of those other days). You then know that the total will be this number plus three (as you have the first three days to think about as well).

If you're wondering how to find out how many 6 machine days Days 1, 2 and 3 are equal to, then a good approach might be to think of it in terms of machine hours. By the rules of this forum I can't give you the answer so sorry I can't be more clear.
i'm really sorry but what you just said was incredibly confusing
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1 month ago
#11
So the order takes 11days if 6machines working.

Day one only had 3 machines working so works out as only half the production for that day.

If you add up the machines that were working for the first three day you get 3 4 5=12,
which is equivalent to only how many days of full production?
Last edited by GabiAbi84; 1 month ago
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#12
(Original post by GabiAbi84)
So the order takes 11days if 6machines working.

Day one only had 3 machines working so works out as only half the production for that day.

If you add up the machines that were working for the first three day you get 3 4 5=12,
which is equivalent to only how many days of full production?
8?
0
1 month ago
#13
(Original post by GabiAbi84)
So the order takes 11days if 6machines working.

Day one only had 3 machines working so works out as only half the production for that day.

If you add up the machines that were working for the first three day you get 3 4 5=12,
which is equivalent to only how many days of full production?
Bold section above was what I was driving at with this question below OP. Day 1 is equivalent to 1/2 of a 6 machine day, as the machines all work at equal rates. Using this approach, what are Day 2 and Day 3 equal to in terms of 6 machine days?
(Original post by Zoqua)
Not quite. How many days with 6 machines working is a day with 3 machines working equal to, in terms of production?
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#14
(Original post by Zoqua)
Bold section above was what I was driving at with this question below OP. Day 1 is equivalent to 1/2 of a 6 machine day, as the machines all work at equal rates. Using this approach, what are Day 2 and Day 3 equal to in terms of 6 machine days?
so day 2 is equivalent to ⅔ of a 6 machine day and day 3 is equivalent to ⅚ of a 6 machine day?
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1 month ago
#15
(Original post by UrGrandpap)
so day 2 is equivalent to ⅔ of a 6 machine day and day 3 is equivalent to ⅚ of a 6 machine day?
Yes . So now that you have this, how many 6 machine days are days 1, 2 and 3 combined?
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#16
(Original post by Zoqua)
Yes . So now that you have this, how many 6 machine days are days 1, 2 and 3 combined?
2?
0
1 month ago
#17
(Original post by UrGrandpap)
12?
Is this your answer to the whole question? Or to the number of 6 machine days that days 1, 2 and 3 are equal to?
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#18
(Original post by Zoqua)
Is this your answer to the whole question? Or to the number of 6 machine days that days 1, 2 and 3 are equal to?
i put 12 for the answer of day 1, 2 and 3 but i don't think it's right.
0
1 month ago
#19
1
1 month ago
#20
(Original post by UrGrandpap)
i put 12 for the answer of day 1, 2 and 3 but i don't think it's right.
You know that Day 1 is 1/2, Day 2 is 2/3, Day 3 is 5/6 in terms of 6 machine days. So you know that days 1, 2 and 3 are equal to 1/2 + 2/3 + 5/6 = 2, so you know the first 3 days are equal to 2 days of 6 machines working.

You know that it takes 11 days of 6 machines working to finish the boxes, so how many extra days are there (and so what is the answer to the question)?
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