P6 Maths
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Thank You for your help.
1) Container A, measuring 30cm by 20cm by 30cm, is 4/5 full of water. Container B, whose base measures 20cm by 20cm, is empty. After transferring some water from Container A to Container B at a constant rate for 40 seconds, Container A becomes 2/3 full. At what rate is the water being transferred to Container B?
2) If Susan works together with Annie, they will take 10 days to produce an art piece. If the two girls work together for 4 days, followed by Susan working alone for 10 days, Annie will take 5 days to complete the remaining work. How long will each girl take to produce the same art piece without the involvement of the other party?
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30 x 20 x 30 x 4/5 = 14400
30 x 20 x 30 x 2/3 = 12000
14400 - 12000 = 2400
2400 / 40 = 60cm^3 / secondHopefully it's right, I haven't touched Pri Maths for some time already.
As for Q2, sorry, lazy to think. (",) -
assume both girls has same work rate.
15 days working alone equal to 6 days working together.
25 days working alone equal 10 days working together
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Originally posted by skythewood:
assume both girls has same work rate.
15 days working alone equal to 6 days working together.
25 days working alone equal 10 days working together
wrong
Susan will take 50 days
Annie will take 12.5 days -
Originally posted by eagle:
wrong
Susan will take 50 days
Annie will take 12.5 days
Is it?Susan + Annie = 4 days
Assume Susan and Annie work together:
Susan (10)+ Annie (5) = 5 days (5 days + 5 days)
Susan (5) = 5 days (equivalent to 1 day working together)
Since it takes 10 days together to complete the art piece, therefore the remaining 1 day is attributable to Susan's 1 day.
Since Susan's 5 days is equivalent to 1 day working together, therefore the 5 days that they work together 1 day is attributable to Susan's 5 days. The remaining 4 days together all belongs to Annie, she spent 5 days, which is 5/4.
Susan's 10 days = 10 / 5 = 2 days work
Annie's 10 days = 10 / (5/4) = 8 days work
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Originally posted by eagle:
wrong
Susan will take 50 days
Annie will take 12.5 daysnow the question is, do we assume they have same work rate or not?
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Originally posted by maurizio13:
Is it?Susan + Annie = 4 days
Assume Susan and Annie work together:
Susan (10)+ Annie (5) = 5 days (5 days + 5 days)
Susan (5) = 5 days (equivalent to 1 day working together)
Since it takes 10 days together to complete the art piece, therefore the remaining 1 day is attributable to Susan.
Since Susan's 5 days is equivalent to 1 day working together, therefore the 5 days that they work together 1 day is attributable to Susan's 5 days. The remaining 4 days together all belongs to Annie, she spent 5 days, which is 5/4.
I lazy to check...
My answer comes from algebra, not sure if P6 level will have learned before
Let work rate (per day) of Susan be S
Let work rate (per day) of Annie be Athus, 6S + 6A = 10S + 5A
So A = 4SSo, 6 days of work by 2 person = 10S + 5A = 30S
1 day of work by 2 person = 5S
10 days of work by 2 person = 50SSo Susan will take 50 days.
Annie will take 50/4 = 12.5 days -
Originally posted by skythewood:
now the question is, do we assume they have same work rate or not?
simple proof that your answer is wrong.
If both take 25 days,
work rate of each person will be 1/25 house per day
which means if 2 persons combined, it will be 2/25 house per day
which means 2 persons combined will need 12.5 days to complete. Obviously wrong since it is already stated to be 10 days :D -
Originally posted by eagle:
I lazy to check...
My answer comes from algebra, not sure if P6 level will have learned before
Let work rate (per day) of Susan be S
Let work rate (per day) of Annie be Athus, 6S + 6A = 10S + 5A
So A = 4SSo, 6 days of work by 2 person = 10S + 5A = 30S
1 day of work by 2 person = 5S
10 days of work by 50SSo Susan will take 50 days.
Annie will take 50/4 = 12.5 daysI am not sure if they learn algebra, because I have a friend teaching primary school tuition, he ask me questions before and told me not to use algebra.
I can't even remember if I learnt it in primary school, I think I did. *shrugs*
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Originally posted by maurizio13:
Is it?Susan + Annie = 4 days
Assume Susan and Annie work together:
Susan (10)+ Annie (5) = 5 days (5 days + 5 days)
Susan (5) = 5 days (equivalent to 1 day working together)
Since it takes 10 days together to complete the art piece, therefore the remaining 1 day is attributable to Susan.
Since Susan's 5 days is equivalent to 1 day working together, therefore the 5 days that they work together 1 day is attributable to Susan's 5 days. The remaining 4 days together all belongs to Annie, she spent 5 days, which is 5/4.
Susan's 10 days = 10 / 5 = 2 days work
Annie's 10 days = 10 / (5/4) = 8 days work
ok, here's how i interpret the question.
2) If Susan works together with Annie, they will take 10 days to produce an art piece. If the two girls work together for 4 days, followed by Susan working alone for 10 days, Annie will take 5 days to complete the remaining work. How long will each girl take to produce the same art piece without the involvement of the other party?
so, 10 days working together
equal 4 day working together +susan work 10 days + Annie work 5 days.
hence, 6 day work together equal 15 day work alone
10 day work together equal 25 day work alone.
i have to assume they have same work rate because there's no indication how much each work is done by each girl individually.
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Originally posted by maurizio13:
I am not sure if they learn algebra, because I have a friend teaching primary school tuition, he ask me questions before and told me not to use algebra.
I can't even remember if I learnt it in primary school, I think I did. *shrugs*
This question can convert easily to bar charts from algebra... but I lazy that's all :D
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Originally posted by eagle:
simple proof that your answer is wrong.
If both take 25 days,
work rate of each person will be 1/25 house per day
which means if 2 persons combined, it will be 2/25 house per day
which means 2 persons combined will need 12.5 days to complete. Obviously wrong since it is already stated to be 10 days :Dwork together is faster than work alone. synergy
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Originally posted by skythewood:
work together is faster than work alone. synergy
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Try that in exams
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Originally posted by eagle:
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Try that in exams
ask the TS for answers.
my method uses ratio to determine the answer, under two simple assumptions.
1)both girl same work rate
2)work together faster than work alone
the thing tested is ratio, or bar chart, a topic expected of p6
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Originally posted by skythewood:
ask the TS for answers.
my method uses ratio to determine the answer, under two simple assumptions.
1)both girl same work rate
2)work together faster than work alone
the thing tested is ratio, or bar chart, a topic expected of p6
my method has no assumptions
and assumption 1 is already wrong
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Originally posted by eagle:
my method has no assumptions
and assumption 1 is already wrong
you make the assumption that working together will not have a higher work rate than working alone
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Originally posted by skythewood:
you make the assumption that working together will not have a higher work rate than working alone
There's no such thing in P6 maths.
You might as well say if there are many more pple, it might be slower because many cooks spoil the broth as well
Please don't confuse people who are seeking for help here. Thanks.
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Originally posted by eagle:
There's no such thing in P6 maths.
You might as well say if there are many more pple, it might be slower because many cooks spoil the broth as well
Please don't confuse people who are seeking for help here. Thanks.
very well.
you can say my assumptions is not practical, but not say my answer is wrong.
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Originally posted by skythewood:
very well.
you can say my assumptions is not practical, but not say my answer is wrong.
it's wrong for P6 Maths
Look at the title
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Originally posted by eagle:
it's wrong for P6 Maths
Look at the title
depends on how they interpret the question to mean both girls have same work rate or different work rate.
if they assume same work rate, than they will have to work on the basis of ratio.
if they assume diff work rate, than they will work on the basis of graphs.
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same work rate already wrong, as I have proved mathematically to you.
and no, don't go and tell me synergy things again. Put yourself in the shoes of the P6 kid who is going to answer this question in exams, and in the shoes of the marker.
I know someone who did this in physics. When asked to explain the motion of free fall when something drops, or something like this, his reply was it depends, and he gave the example of the movie Matrix, where you do not fall at 9.81 m/s^2, but can hang in mid-air
=> He didn't get 0 marks; he got -1 marks.So, please do not confuse students looking for genuine help here. We can well do less with such cases as above. Thanks.
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-- edited post away for purposely confusing students --
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Annie will take 12.5 days while Sarah will take 50 days.
Haha, dunno how to draw out the model here.
But after u drew out the model, u can come out with an equation,
10S + 5A = 6(S+A)
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.
.
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and u will found out that Sarah speed is 1/4 of Annie's
Which means that Annie complete 8/10 of the artwork while Sarah complete 2/10 of it.
Therefore, if working alone,
Sarah would take 10/2 *10 = 50 days
Annie would take 10/8 *10 = 12.5days
Not sure if pri 6 are able to solve this kind of equation but I do know that algebra has been added into pri 6's syllabus.
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Originally posted by fately:
Annie will take 12.5 days while Sarah will take 50 days.
Haha, dunno how to draw out the model here.
But after u drew out the model, u can come out with an equation,
10S + 5A = 6(S+A)
.
.
.
.
and u will found out that Sarah speed is 1/4 of Annie's
Which means that Annie complete 8/10 of the artwork while Sarah complete 2/10 of it.
Therefore, if working alone,
Sarah would take 10/2 *10 = 50 days
Annie would take 10/8 *10 = 12.5days
Not sure if pri 6 are able to solve this kind of equation but I do know that algebra has been added into pri 6's syllabus.
than use algebra loh
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1) Vol of A = 30x20x30 = 18000cm^3
Before pouring: 4/5 x 18000 = 14400cm^3
After pouring: 2/3 x 18000 = 12000cm^3
Vol transferred = 14400 - 12000 = 2400cm^3
Rate = 2400 / 40 = 60cm^3/s
2) Let the rate of Susan be s and rate of Annie be a. Let the art piece be 1.
10(s+a) = 10s + 10a = 1 [a = (1-10s)/10]
4s + 4a + 10s + 5a = 1
14s + 9a = 1
14s + 9/10 - 9s = 1
5s = 1/10
s = 1/50
a = (1 - 10/ 50) / 10 = 2/25
Therefore, Susan takes 50 days and Annie takes 12.5 days.