Q&A - PSLE Math

[Denise]

[Moderator's note: Topics merged.]


The Distance between Town A and Town B was 100km. At 7am, Ali left Town A and cycle towards Twon B . Half an hour later, Grace left at the same place and cycle towards Town B. Grace travelling speed was 4km/h faster than Ali. At 11am , Grace caught up with Ali. When Grace was 10km away from Town B, she stopped to wait for Ali. How far was Ali from Grace when she stopped to wait for him?

[tianzhu]

Denise:

The Distance between Town A and Town B was 100km. At 7am, Ali left Town A and cycle towards Twon B . Half an hour later, Grace left at the same place and cycle towards Town B. Grace travelling speed was 4km/h faster than Ali. At 11am , Grace caught up with Ali. When Grace was 10km away from Town B, she stopped to wait for Ali. How far was Ali from Grace when she stopped to wait for him?

Hi, just to check

A to B -->100km
Start at 7am(Ali) and 730am(Grace)
Meet at 11am
Please confirm these figures.

I may be wrong,but my draft calculation showed that Ali cycled at 28km/h and Grace at 32 km/h.For them to meet at 11am, the distance travelled would be 112km.

[Dharma]

tianzhu:

Denise:

The Distance between Town A and Town B was 100km. At 7am, Ali left Town A and cycle towards Twon B . Half an hour later, Grace left at the same place and cycle towards Town B. Grace travelling speed was 4km/h faster than Ali. At 11am , Grace caught up with Ali. When Grace was 10km away from Town B, she stopped to wait for Ali. How far was Ali from Grace when she stopped to wait for him?

Hi, just to check

A to B -->100km
Start at 7am(Ali) and 730am(Grace)
Meet at 11am
Please confirm these figures.

I may be wrong,but my draft calculation showed that Ali cycled at 28km/h and Grace at 32 km/h.For them to meet at 11am, the distance travelled would be 112km.

You are right Tianzhu ....some problem with the figures in the Qn

[Vanilla Cake]

_jas_:

Hi help needed for these questions! ASAP pls as my child has an exam coming up!!


1) A bus left town A for town B at a speed of 45km/h. At the same time, a van left Town B for Town A at the speed of 55km/h. Both vehicles travelled along the same road. how far apart were they 1 hour before they met (ans:100km)

2) At 09 00, a van left Town P for Town Q. After some time, a car left Town Q for Town P. The two vehicles met at 11 30. The ratio of the average speed of the van to the average speed of the car is 3:5.
a) What time did the car leave town Q (ans:10 00)
b) If the distance between town P and Town Q is 150 km, calculate the average speed of the van. (ans:30km/h)

3) The ratio of the amount of water in Bottle A to the amount of water in Bottle B was 2:1. After 60ml of water was pured into Bottle A and 150ml was poured out of bottle B, the ratio became 4:1.
What was the amount of water in bottle A at first? (Ans:660)

TIA!

tianzhu:

As for Q2, you may wish to check your question again.Is there any missing information such as meeting at midway?

For Info:
Q1 - Raffles Girls' Primary School - P6 Maths SA1 (2008) - Q33
Q2 - Raffles Girls' Primary School - P6 Maths SA1 (2008) - Q48
Q3 - Raffles Girls' Primary School - P6 Maths SA1 (2008) - Q42

Q2 as appeared in the paper http://www.wendykoh.com/08/primary6-rgssa1-maths.pdfType password as \"abc123\" and go to page 24 for Q48.
At 09 00, a van left Town P for Town Q. After some time, a car left Town Q for Town P. The two vehicles met midway at 11 30. The ratio of the average speed of the van to the average speed of the car is 3:5.
a) What time did the car leave town Q?
b) If the distance between town P and Town Q is 150 km, calculate the average speed of the van.

[wmd]

tianzhu:

The answers given in the worksheet are a) 7:1:8 and b) 168.

But, my answer for a) was 7:11:9. You may want to try it out.

(Ai Tong School P6 SA1 Q43 - 2007)
Packets of assorted candies were sold in 2 different sizes - standard and large. The large packet contained twice as many candies as the standard packet. In the standard packet, the ratio of the number of coconut candies to the number of strawberry candies were 4:5. In the large packet, the ratio of the number of coconut candies to the number of strawberry candies to the number of toffee candies was 1: 2: 3.

A family bought 1 standard and 1 large packet.

(a) What was the ratio of the number of coconut candies to the number of strawberry candies to the number of toffee candies?

(b) The family ate 21 candies. As a result, the ratio of the number of coconut candies to the number of strawberry candies to the number of toffee candies became 2: 3: 3. How many candies were left?

Large packet
c:s:t
= 1:2:3

Standard packet
c:s
4:5

Large packet contains 2x as many candies as standard packet.
No. of units (standard packet) = 9
no. of units (large packet) = 9 *2 = 18
therefore, c:s:t = 3:6:9

(a) 1 standard + 1 large, c:s:t = 7:11:9

(b)
before eating : c:s:t = 7:11:9
after eating 21 candies, c:s:t = 2:3:3 = 6:9:9

No toffee candies are eaten
18u - 15u = 21
3u = 21
u =7
candies left = 24*7 = 168.

I saw this post just now, frankly speaking, it was a good question, answer was correct too, but I would like to highlighted here is that the solution is not reasonable.

Right solution is:
3u+8v=21, (2v+3v+3v=8v), here u, v are whole numbers.
hence, only one solution for above equation, u=7, v=0.


if family ate 31 candies instead, by solving the equation 3u+8v=31, we got u=5 and v=2. of course, it is more challenger than original question, it is a Math Olympiad Question, I think.

[faith2u]

[Moderator's note: Topics merged.]


1). A box contains red and yellow ribbons. There are six times as many red ribbons as yellow ribbons. When 75 red ribbons are removed and 75 yellow ribbons are added, there will be 20 more yellow ribbons than red ribbons. What is the total number of red and yellow ribbons in the box at first?

2). Mrs Joyce used a container to hold some rice. At first, the empty container was 1/8 as heavy as the rice. After selling 60kg of rice, the empty container becomes 3/4 as heavy as the remaining rice. How many kilograms of rice did Mrs Joyce are at first?

3). Alice had a sum of money. She gave $800 to her parents and spent $360 on an electronic dictionary. She then donated 0.25 of her remaining money equally to 5 charities. She had 9/20 of her original sum of money left. Find the amount of money each of the 5 charities received.

4). Mr Andrew started his journey from Singapore to KL. After completing 2/9 of the \tjourney, he overtook a bus, which was travelling at a uniform speed of 80km/h in the same direction. When Mr Andrew reached KL 3 hours after overtaking the bus, the bus still had another 82km to travel before reaching KL. If Mr Andrew travelled at an average speed of 90km/h, how long did he take to arrive at KL? Give your answer in hours and minutes.


Thanks in advance.

[kiasiparent]

Vanilla Cake:

_jas_:

Hi help needed for these questions! ASAP pls as my child has an exam coming up!!


1) A bus left town A for town B at a speed of 45km/h. At the same time, a van left Town B for Town A at the speed of 55km/h. Both vehicles travelled along the same road. how far apart were they 1 hour before they met (ans:100km)

2) At 09 00, a van left Town P for Town Q. After some time, a car left Town Q for Town P. The two vehicles met at 11 30. The ratio of the average speed of the van to the average speed of the car is 3:5.
a) What time did the car leave town Q (ans:10 00)
b) If the distance between town P and Town Q is 150 km, calculate the average speed of the van. (ans:30km/h)

3) The ratio of the amount of water in Bottle A to the amount of water in Bottle B was 2:1. After 60ml of water was pured into Bottle A and 150ml was poured out of bottle B, the ratio became 4:1.
What was the amount of water in bottle A at first? (Ans:660)

TIA!

tianzhu:

As for Q2, you may wish to check your question again.Is there any missing information such as meeting at midway?

For Info:
Q1 - Raffles Girls' Primary School - P6 Maths SA1 (2008) - Q33
Q2 - Raffles Girls' Primary School - P6 Maths SA1 (2008) - Q48
Q3 - Raffles Girls' Primary School - P6 Maths SA1 (2008) - Q42

Q2 as appeared in the paper http://www.wendykoh.com/08/primary6-rgssa1-maths.pdfType password as \"abc123\" and go to page 24 for Q48.
At 09 00, a van left Town P for Town Q. After some time, a car left Town Q for Town P. The two vehicles met midway at 11 30. The ratio of the average speed of the van to the average speed of the car is 3:5.
a) What time did the car leave town Q?
b) If the distance between town P and Town Q is 150 km, calculate the average speed of the van.

Q2 was a maths olympiad question last time. Now it has become a rather common question in maths syllabus question.

Speed Van: Car = 3:5
Time Van: Car = 5units :3 units

Since they travelled the same distance(midway), the time taken by the van will be 5 units and the car will be 3 units respectively.

11.30 - 9.00= 2 hours 30mins

5 units = 2 hours 30 mins
1 unit = 30mins
3 units = 1 hour 30 mins

So the car leave town Q at 11.30 - 1.30 = 10.00am

(b) 150 / 2 = 75
75 / 2.5hours = 75 x 2/5 = 30 km/h

[tianzhu]

faith2u:

[Moderator's note: Topics merged.]


4). Mr Andrew started his journey from Singapore to KL. After completing 2/9 of the \tjourney, he overtook a bus, which was travelling at a uniform speed of 80km/h in the same direction. When Mr Andrew reached KL 3 hours after overtaking the bus, the bus still had another 82km to travel before reaching KL. If Mr Andrew travelled at an average speed of 90km/h, how long did he take to arrive at KL? Give your answer in hours and minutes.

Hi
Q4 can be solved using this approach.

In 3 hrs, the bus travelled 240km.It is still 82km away from KL.
Therefore, 7 units of the journey is 322km

Distance between Sin and KL --- 414km
Time taken by Andrew ---414/90 ---4.6 h --- 4h 36min

But there are some discrepancies,in 3h, Andrew travelled 3*90 --- 270km which is not equal to 322km.

[Vanilla Cake]

1). A box contains red and yellow ribbons. There are six times as many red ribbons as yellow ribbons. When 75 red ribbons are removed and 75 yellow ribbons are added, there will be 20 more yellow ribbons than red ribbons. What is the total number of red and yellow ribbons in the box at first?


A1.
Draw a model and you will see that
5 units->(75-20)+75
=55+75
=130
1 unit -> 130/5 = 26
7 units-> 26x7 = 182

Total number of red and yellow ribbons is 182
( Red ribbon is 156 and yellow ribbon is 26 )

2). Mrs Joyce used a container to hold some rice. At first, the empty container was 1/8 as heavy as the rice. After selling 60kg of rice, the empty container becomes 3/4 as heavy as the remaining rice. How many kilograms of rice did Mrs Joyce are at first?

A2.
Before
C : R
1 : 8 ( Multiply by 3 )
3 : 24

After
C : R
3 : 4

20 units-> 60 kg
1 unit -> 3 kg
24 units -> 72 kg

At first, amount of rice that Mrs Joyce had 72 kg.

3). Alice had a sum of money. She gave $800 to her parents and spent $360 on an electronic dictionary. She then donated 0.25 of her remaining money equally to 5 charities. She had 9/20 of her original sum of money left. Find the amount of money each of the 5 charities received.

A3.
Draw a model and you will see that :
9 parts for amount of money left, 3 parts for charity and 8 parts for money given to parents and spent on electronic dictionary.

20-12 = 8
8 units-> 800+360 = 1160
1 unit = 145
3 units= 435
5 charities -> $ 435
1 charity -> $ 87
Amount of money that each of the 5 charities received was $ 87

4). Mr Andrew started his journey from Singapore to KL. After completing 2/9 of the \tjourney, he overtook a bus, which was travelling at a uniform speed of 80km/h in the same direction. When Mr Andrew reached KL 3 hours after overtaking the bus, the bus still had another 82km to travel before reaching KL. If Mr Andrew travelled at an average speed of 90km/h, how long did he take to arrive at KL? Give your answer in hours and minutes.

A4.
7/9 of the journey-> 80x3 + 82 = 322 km
Total distance -> 322/7x9 = 414 km
Time taken => 414/90 = 4 & 3/5 h = 4 h 36 min

Time taken for Mr Andrew to arrive at KL was 4 h 36 min

I tried working backwards and find it strange.
7/9 of the journey (bus)-> (80x 3) +82 = 322 km
7/9 of the journey (car) -> 90x 3 = 270 km
By right, both figures should be the same.Where did you get this question from? :?

[Dharma]

faith2u:

[Moderator's note: Topics merged.]


1). A box contains red and yellow ribbons. There are six times as many red ribbons as yellow ribbons. When 75 red ribbons are removed and 75 yellow ribbons are added, there will be 20 more yellow ribbons than red ribbons. What is the total number of red and yellow ribbons in the box at first?

2). Mrs Joyce used a container to hold some rice. At first, the empty container was 1/8 as heavy as the rice. After selling 60kg of rice, the empty container becomes 3/4 as heavy as the remaining rice. How many kilograms of rice did Mrs Joyce are at first?

3). Alice had a sum of money. She gave $800 to her parents and spent $360 on an electronic dictionary. She then donated 0.25 of her remaining money equally to 5 charities. She had 9/20 of her original sum of money left. Find the amount of money each of the 5 charities received.

4). Mr Andrew started his journey from Singapore to KL. After completing 2/9 of the \tjourney, he overtook a bus, which was travelling at a uniform speed of 80km/h in the same direction. When Mr Andrew reached KL 3 hours after overtaking the bus, the bus still had another 82km to travel before reaching KL. If Mr Andrew travelled at an average speed of 90km/h, how long did he take to arrive at KL? Give your answer in hours and minutes.


Thanks in advance.

Q3

If 9/20 of original amt of money is left, then 11/20 of original amt used up ($800 + $360 +1/4 of Remainder[R])

3/4R ----9/20
1/4R ----3/20

1/4R + $1160 .....11/20
8/20 ----$ 1160
3/20 ----$145 (Total amt given to 5 charities)

1 charity gets -----$145/5 = $29