Tutor MathsGuru: Ask me for your burning Maths questions!

[Dharma]

last minute mama:

Dear Dharma,


Thanks for your prompt response. I could not understand why the equation is x+7 + 7 = 20?

After they met at P,
x+7+7 is distance travelled by Raju
x + 10 + 10 is distance travelled by Ali
When they meet again at Q (7 km from Town B)?

Not sure how this works. Please explain.

This is a meeting problem of 2 persons leaving at the same time and moving towards each other. When they meet, the time taken by Raju and Ali is the same.
When they meet for the first time at P, the total distance travelled by Raju and Ali is actually the distance between the 2 towns .

When they meet for the 2nd time at Q, both take equal time to travel from P to Q (point where they meet again)
Raju travels X km (from P to Q) + 7 km ( Q to Town B ) + 7km ( Town B to Q) while Ali travels 10km ( P to Town A) + 10km ( Town A to P ) + X km ( P to Q)

The ratio of the distances travelled by Raju and Ali will be the every time they newer before the time they take is the same to meet.
However, when the meet at Q, the total distance covered by Raju and Ali will be 2 times the distance of Town A and Town B.
Therefore total distance trvelled by Raju from P to Q ( point where he met Ali) will double to 20km

so, X + 7 + 7 = 20
X = 6

distance travelled by Ali when he met Raju at P for the 1st time is 13km ( 7 + 6) km.

You will realize that of u work out Ali will travel another 13km x 2 = 26km before he meets Raju at Q for the 2nd time.

20km + 26km = 46km ( twice the distance between Town A and B)

This qn is quite similar to 2 persons on opposite end of a circular track and running towards each. When they meet for the 1st time they would have run half the circumference of the track and when they meet for the 2nd time they would have covered the circumference of the track in total.

[CJM]

Vanilla Cake:

CJM:

Dave had 59 toy cars and toy soldiers. After giving away 1/3 of his toy cars and 4 of his toy soldiers, he had an equal number of toy cars and toy soldiers. How many toy soldiers did he have at first ?

TC: Toy cars
TS: Toy soldiers

TC: [][][]
TS: [][][4]

[][][]+[][][4]=59
5[]=59-4=55
[]=11

Toy soldiers (at first) = [][]+4 = 2x11+4=26

Check
At first
Toy cars: 3x11=33
Toy soldiers: 2x11+4=26

Change
Gave away 1/3 of his toy cars and 4 of his toy soldiers.
1/3 of toy cars = 1/3x33=11

In the end
Toy cars: 33-11=22
Toy soldiers: 26-4=22

22=22
In the end, Dave had an equal number of toy cars and toy soldiers.

vanilla cake, thank u for the detailed explanation : )

[tianzhu]

[quote]However, when the meet at Q, the total distance covered by Raju and Ali will be 2 times the distance of Town A and Town B. [/quote]
Hi Dharma

Good Morning

They met at the third period of time, I think the total distance covered by by Raju and Ali will be 3 times the distance of Town A and Town B instead of 2 if we take reference from the starting points.

Best wishes

[tianzhu]

Hi Dharma


This question is quite similar to Rosyth 2008 SA2 Q48.

Ning and Zongwei jogged to and fro repeatedly along a straight path in a park between two points A and
B. Ning jogged at a uniform speed of 4 m/s and Zongwei jogged at a uniform speed of 6 m/s. They
started jogging from opposite directions at the same time as shown below.
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 160m. Find the distance between A and B.
b) If they started jogging at 8 am, how long did they take to meet again for the third time? (Express
answers in min and seconds).

However in the Rosyth question, the speed ratios are given.

In this question, the speeds of Raju and Ali are not given.

Do we have to make an assumption that they turn at the third interval of time?

Best wishes.

[Dharma]

tianzhu:

[quote]However, when the meet at Q, the total distance covered by Raju and Ali will be 2 times the distance of Town A and Town B.

Hi Dharma

Good Morning

They met at the third period of time, I think the total distance covered by by Raju and Ali will be 3 times the distance of Town A and Town B instead of 2 if we take reference from the starting points.

Best wishes[/quote]Good Morning Tianzhu,

If Raju and Ali met for the 2nd time at Point Q, Raju would have travelled 3 times the distance he travelled from Town A to Point P when they met for the 1st time.

From P to Q (Both meeting points); Raju travelled 20km (6 + 7 + 7)km while Ali travelled 26km (10 + 10 + 6)km

Total distances travelled by Raju & Ali from the 1st time they met to the 2nd time they met
= 20km + 26km = 46km

46km is 2 times the distance between Town A and Town B.

You are correct to say that the total distances covered by Raju and Ali when they met for the 2nd time at Q based on their initial starting points i.e. at Town A and Town B will be 69km which is 3 times the distance between Town A and Town B.

[Dharma]

tianzhu:

Hi Dharma


This question is quite similar to Rosyth 2008 SA2 Q48.

Ning and Zongwei jogged to and fro repeatedly along a straight path in a park between two points A and
B. Ning jogged at a uniform speed of 4 m/s and Zongwei jogged at a uniform speed of 6 m/s. They
started jogging from opposite directions at the same time as shown below.
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 160m. Find the distance between A and B.
b) If they started jogging at 8 am, how long did they take to meet again for the third time? (Express
answers in min and seconds).

However in the Rosyth question, the speed ratios are given.

In this question, the speeds of Raju and Ali are not given.

Do we have to make an assumption that they turn at the third interval of time?

Best wishes.

In the Rosyth 2008 qn, part (b) requires the pupil to calculate the time taken for Ning and Zoingwei to meet to for the 3rd time. However, the current question only talks about Raju and Ali meeting twice. So, we don’t need to assume that they turn around for the 3rd time.

Both questions are similar but the information given in both questions are different. Rosyth qns gives the speed of the 2 persons and the distance between the meeting points, X and Y while the current question requires us to find out the distance between the 2 meeting points.

[tianzhu]

Hi Dharma


Thank you for your reply.

I think we are not talking about the same thing. I am sorry for not making it clear in my earlier post.

Let’s not focus in what were asked to find in the Rosyth question.

I brought it up to show the similarity between the Rosyth and the new question in certain aspects.

The ratios in one question are given while in the other, they are not.

If the speed ratios are given, a student can easily show that they would meet at the third period of time.

The question is how does one knows that they’ll meet at the third period of time if the speed ratios are not given?

In the third interval of time, Raju makes a U turn, do we assume that he does it at the third period?

If we make an assumption that they would meet at the third period of time, then this question could be solved with visual representation by showing a distance line.

Best wishes

[Dharma]

tianzhu:

Hi Dharma


Thank you for your reply.

I think we are not talking about the same thing. I am sorry for not making it clear in my earlier post.

Let’s not focus in what were asked to find in the Rosyth question.

I brought it up to show the similarity between the Rosyth and the new question in certain aspects.

The ratios in one question are given while in the other, they are not.

If the speed ratios are given, a student can easily show that they would meet at the third period of time.

The question is how does one knows that they’ll meet at the third period of time if the speed ratios are not given?

In the third interval of time, Raju makes a U turn, do we assume that he does it at the third period?

If we make an assumption that they would meet at the third period of time, then this question could be solved with visual representation by showing a distance line.

Best wishes

Hi Tianzhu,

For this question, when they meet for the 1st time, both take the same time (fixed time).
We found out that Town A to P is 10km and Town B to P is 13km. So, the distance ratio of Raju : Ali = 10 : 13 and their speed ratio will also be 10 : 13. The speed ratios will ontinue to be the same so long as they do not change their speeds.

They will meet for the 3rd time, 4th time and so on if they continue moving back and forth between Town A and Town B.

If they set off from the same point but in opposite directions, their total distance from the time they move to the time they meet again will be twice the sum of the total distance of Town A and Town B.

“ In the third interval of time, Raju makes a U turn, do we assume that he does it at the third period? “.Yes.

If they continue their travelling they will meet at Point R which is 4km from Town A and it can be seen by drawing a distance line.

[tianzhu]

Dharma:

“ In the third interval of time, Raju makes a U turn, do we assume that he does it at the third period? “.Yes.

Hi Dharma

Thank you for your reply.

The starting point is to make an assumption that they turn at the third period of time.

Once a student is able to do it, this question could be easily solved by drawing a distance line.

Best wishes

[peapot]

Hi, I have encounter a P1 math problem. Please see pic below. I found out the answer by trial and error but is there a systematic approach to solve this question. I do not understand how to teach my P1 gal on this type of question. Please help me!

Thanks!!


http://postimage.org/image/3393pe1s4/
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