P6 Maths Problem Sum - Rosynth Prelim Paper 2008
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Hi ! Here is a Rosynth School's P6 problem sum that is to be solved using non-algebra method.
Ning and Zhongwei jogged to and fro repeatedly along a straight line in a park between two points A and B. Ning jogged at a uniform speed of 4m/s and Zhongwei jogged at a uniform speed of 6 m/s. They started jogging from opposite directions at the same time as shown below.
Ning @ 4m/s ----> <----------Zhongwei @6m/s
X Y
A ----------------------|----------------------------------|--------------------------B
They first met one another at point X. The second time they met was at point Y.
a) Given that the distance between X and Y is 160 m . Find the distance between A and B.
b) If they started jogging at 8 a.m. , how long did they take to meet again for the 3rd time? (Express your answers in minutes and seconds)
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erm. how in theory do they meet two times?
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Originally posted by loki_chaos:
erm. how in theory do they meet two times?
1 goes from A to B back to A then to B again while the other goes from B to A back to B then to A again
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Edit: opppsss read wrongly thought AB was 160m hahaha. Have corrected solution. :P
Distance travelled for Ning:Zhongwei = 3:2
For 1st meeting:
Ning travelled = AX
Zhongwei travelled = XY = 160 + BY
This is illustrated in yellow diagram
For 2nd meeting
Ning travelled = XY + BY = (160+BY) + BY = 160 + BY + BY
Zhongwei travelled = AX + AY = AX + AX +160
This is illustrated in the plain diagram.
LCM = 30 so converted all ratio to create total parts of 30.
6 parts = 160m
30 parts = 160m x5 = 800m
30 parts = double the total distance
Thus AB = 400m
Thus we know that
AX =160, XY=160, YB=80
Time for 1st meet
= 400/10 = 40s
Distance travelled by Ning between 1st and 2nd meet
= 160+80+80
= 320
Time between 1st and 2nd meet
= 320/4 = 80s
After 2nd meet...
Zhongwei reached B
= 80/6 = 40/3 s
Ning is now
= 80 + (40/3 x 4)
= 400/3 m away from B aka 800/3m from A
Ning reached A
= (800/3)/4
=66 2/3 seconds later
Zhongwei is now...
= 66 2/3 x6
= 400m from B aka at A
Time lapsed from start
= 40+80+ 40/3 + 66 2/3
= 200s
3mins 20sec
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Originally posted by Mikethm:
Relative velocity when running in opposite direction = 4 + 6 = 10m/s
Relative velocity when running in same direction = 6-4 = 2m/s
1st meeting
160/10 = 16s
Distance travelled by Ning = 16 x4 = 64m
X = 64m from A
Zhongwei reach A 10 2/3 second from 1st meet.
Ning reach B 24 seconds from 1st meet.
Zhongwei is now (13 1/3 x 6) = 80m from A.
Distance between Ning and Zhongwei is now 80m
They meet 8s from THIS moment.
Y = 8 x 4 = 32m from B
Distance AB = 160-64-32 = 66m
Zhongwei reach B 5 1/3 second from 2nd meet.
Ning is now 32 + (5 1/3 x 4) = 53 1/3m from B.
26 2/3 seconds later, Ning reach A.
Zhongwei travelled 26 2/3 x 6 = 160m
They meet at A.
Time lapsed = 16+24+8+(5 1/3 + 26 2/3) = 80s
They meet for the 3rd at 8:01:20... correct or not?
Seow lah. XY is already 160 m and XY is only part of AB. So, how can AB = 66 m
AB cannot be shorter than XY ! Fail ! -
Hi MikeThm,
Ans a) 400m
b) 3 min 20s
Nice Try
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Originally posted by Mikethm:
Edit: opppsss read wrongly thought AB was 160m hahaha. Will attempt later :P
Solution for 1st part upcoming...
Distance travelled for Ning:Zhongwei = 3:2
For 1st meeting:
Ning travelled = AX
Zhongwei travelled = XY = 160 + BY
This is illustrated in yellow diagram
For 2nd meeting
Ning travelled = XY + BY = (160+BY) + BY = 160 + BY + BY
Zhongwei travelled = AX + AY = AX + AX +160
This is illustrated in the plain diagram.
LCM = 30 so converted all ratio to create total parts of 30.
6 parts = 160m
30 parts = 160m x5 = 800m
30 parts = double the total distance
Thus AB = 400m
First thing we need to understand : Time needed for them to meet again and again in terms of units is always the same. When they first meet,
Ning travelled l__l__l__l__l
Zhongwei travelled l__l__l__l__l__l__l
Total distance = l__l__l__l__l__l__l__l__l__l__l
Ning travelled 160m before meeting Zhongwei again, so l__l = 40m
Hence, l__l__l__l__l__l__l__l__l__l__l = 400m
Sometimes we think too hard, don't you think so?
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Originally posted by Forbiddensinner:
First thing we need to understand : Time needed for them to meet again and again is always the same. When they first meet,
Ning travelled l__l__l__l__l
Zhongwei travelled l__l__l__l__l__l__l
Total distance = l__l__l__l__l__l__l__l__l__l__l
Ning travelled 160m before meeting Zhongwei again, so l__l = 40m
Hence, l__l__l__l__l__l__l__l__l__l__l = 400m
Sometimes we think too hard, don't you think so?
Actually you are wrong. For 1st meeting, distance travelled is 400m (1)
For subsequent meeting, it is 800m (2) UNLESS Zhongwei catch up with Ning before Ning can turn around (3).
The long working is to make sure that case (3) did not occur.
In maths, it is best not to assume anything and rigorously test your reasoning process.
In addition, solutions should be explain in an appropriate standard suitable for the audience. Rather long than not understood.
The 400/800m thingie we can reason out... but a 12 years old kid can?
Even at O level... plenty of students does not understand p increased by 300% is 4p, not 3p.
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Originally posted by Seowlah:
Seow lah. XY is already 160 m and XY is only part of AB. So, how can AB = 66 m
AB cannot be shorter than XY ! Fail !You have no rights to scold others if you are not even helping out yourself.
No one here is perfect - even the mods do made what we often known as "simple mistakes" at time. It could be due to fatigue, illness, or some other reasons, but most importantly, everyone have tried their best to help out others.
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Originally posted by Mikethm:
Actually you are wrong. For 1st meeting, distance travelled is 400m (1)
For subsequent meeting, it is 800m (2) UNLESS Zhongwei catch up with Ning before Ning can turn around (3).
The long working is to make sure that case (3) did not occur.
In maths, it is best not to assume anything and rigorously test your reasoning process.
My bad, I seem to be making a lot of mistakes recently.
Looks like I have to try out more questions myself too to prevent my level of "Maths consciousness" from dropping any further.
Edit: I just realise that by looking at my own model, I should have realise that my own working is wrong. This is really a situation in which I deserve a facepalm.
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Originally posted by Forbiddensinner:
My bad, I seem to be making a lot of mistakes recently.
Looks like I have to try out more questions myself too to prevent my level of "Maths consciousness" from dropping any further.
Edit: I just realise that by looking at my own model, I should have realise that my own working is wrong. This is really a situation in which I deserve a facepalm.
No problem. I did even worse than you on my 1st attempt at 1am yesterday. Misread AB as 160m. -
Hi , Mikethm & Forbiddensinner , appreciate your helps for the solutions. Thanks!
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Originally posted by Forbiddensinner:
My bad, I seem to be making a lot of mistakes recently.
Looks like I have to try out more questions myself too to prevent my level of "Maths consciousness" from dropping any further.
Edit: I just realise that by looking at my own model, I should have realise that my own working is wrong. This is really a situation in which I deserve a facepalm.
Seow lah. You have already admitted that you have made a lot of mistakes recently. So, don't try to find excuses for your mistakes anymore lah.
See, Mikethm also makes a mistake and just acknolwdges the mistake and make amend to give the correct answer. This should be the spirit of learning. XD.
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Originally posted by Seowlah:
Seow lah. You have already admitted that you have made a lot of mistakes recently. So, don't try to find excuses for your mistakes anymore lah.
See, Mikethm also makes a mistake and just acknolwdges the mistake and make amend to give the correct answer. This should be the spirit of learning. XD.
You are new here so let me tell you one thing.
Unlike Chit-chat, Club 30 and Tiny Club, we generally do not welcome unconstructive posts here in homework forum, as this is a forum for people to learn, not to spam.
You might have seen many forummers such as ditzy, nikar, marcteng who post all over the sgforums, but do you see them posting here if they know they are not going to help out? No.
And am I finding an excuse? I already said it is my bad, it is my own fault. And most importantly who are YOU to call people Fail when you did not help out yourself?
One should be humble when it comes to learning, but as far as I can tell you are not a teacher but a troll-to-be. I am certainly not interested in learning anything from a troll who is only capable of criticising and is unwilling to help out others.
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Originally posted by Forbiddensinner:
You are new here so let me tell you one thing.
Unlike Chit-chat, Club 30 and Tiny Club, we generally do not welcome unconstructive posts here in homework forum, as this is a forum for people to learn, not to spam.
You might have seen many forummers such as ditzy, nikar, marcteng who post all over the sgforums, but do you see them posting here if they know they are not going to help out? No.
And am I finding an excuse? I already said it is my bad, it is my own fault. And most importantly who are YOU to call people Fail when you did not help out yourself?
One should be humble when it comes to learning, but as far as I can tell you are not a teacher but a troll-to-be. I am certainly not interested in learning anything from a troll who is only capable of criticising and is unwilling to help out others.
Seow lah. your logic is that people cannot point out your mistake when you are trying to help others even when your answer is wrong.
The use of the word fail is just like incorrect. Why are you so sensitive to the word fail ?
You should be like Mikethm. When one makes a mistake, acknowledges the mistake and correct the mistakes and give the correct answer. This should be the spirit of learning.
Strange. Did I say that I want you to learn from me ?
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Originally posted by Seowlah:
Seow lah. your logic is that people cannot point out your mistake when you are trying to help others even when your answer is wrong.
The use of the word fail is just like incorrect. Why are you so sensitive to the word fail ?
You should be like Mikethm. When one makes a mistake, acknowledges the mistake and correct the mistakes and give the correct answer. This should be the spirit of learning.
Strange. Did I say that I want you to learn from me ?
You are not wrong to point out that Mikethm or me is wrong.
But your attitude and tone is that of someone looking for trouble, not someone who is sincerely trying to help out.
As an educator, I strongly advocate against the use of Fail ( With the exception being on exam papers, but that is a reason why we uses "F" instead of "fail" ), regardless of on a student or on others. By telling others they fail, it is as good as telling them that they are failures.
I acknowledge my mistake already, and to begin with, did I say that Mikethm's new workings were wrong? I don't think so. I merely said that I might have found something which is shorter, which turned out to be wrong afterall.
As for you, by using the word "seow", you are being extremely disrespectful and rude to others, and you do not think of that as a fault yourself. You merely pointed out the mistakes of others, what gives you the right to scold them? If anyone needs to apologize, it will be you for your unruly behaviour here.
By telling me this : "When one makes a mistake, acknowledges the mistake and correct the mistakes and give the correct answer. This should be the spirit of learning.", aren't you saying that I should learn from you?
Side Note : Eagle or Wee, "Learning is the way" has already got the correct answers from Mikethm, please close this thread before it becomes a full flaming thread. I apologize for any trouble that I might have caused here.
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Originally posted by Seowlah:
Seow lah. You have already admitted that you have made a lot of mistakes recently. So, don't try to find excuses for your mistakes anymore lah.
See, Mikethm also makes a mistake and just acknolwdges the mistake and make amend to give the correct answer. This should be the spirit of learning. XD.
Hi Seowlah, thanks for your comments.
Forbiddensinner is already very kind to help out; we are all helping out of kindness and are not paid nor given any benefits other than the joy of helping. Do reserve the tone of speech for Speaker's Corner, not here.
In addition, do read part v of our Homework Forum guidelines :D
I shall lock this thread since TS has understood the question.