Q&A - PSLE Math

[tianzhu]

Winx5015:

Hi, can anyone help regarding questions on Speed.


(1). At 9am,Jane and Carol started travelling from Town A to Town B. Jane travelled at an average speed that was 20km/h more than Carol's average speed. At 11am, Jane reached Town Y. How far was Carol from Town Y at that time?

(2). At 9am, Jane and Carol started travelling towards each other from their homes, which were 210km apart. Jane travelled at an average speed that was 20km/h more than Carol's average speed. If they met each other at noon, what was Jane's average speed?

Thank you

Hi

As in any questions on Speed, it’s useful to draw some simple pictorial representations.

Q1) Jane travelled at a speed of 20 km/h faster than Carol.

In 1h, Jane travelled 20 km more than Carol.

From 9am to 11am ------- 2h

2*20 ------40km

Carol was 40 km away when Jane reached Town B.

Q2)It may be helpful to recall the time when daddies and mummies were paktoring.

Imagine daddy at one end of a bridge and mummy standing at the other end. Daddy and mummy ran towards one another and met each other at some point along the bridge. At the moment when they met, they covered the whole length of the bridge.

For them to meet, Jane and Carol must cover a distance equal to the distance between their houses.

From 9am to noon -------- 3h

210/3 ------- 70

Jane’s speed was 20 km/h faster.

In 1h, Jane travelled 20 km more than Carol.

(70 – 20)/2 ------ 25
25+20 ------45

Jane’s speed ------ 45 km/h

Best wishes

[Michaelia0816]

Pls help me with the following question, Tianzhu! 1) A rectangular tank, 1/3 filled with water, has a square base of 4m2. The ratio of its height to its length is 3:5. A tap is turned on and water flows into the tank at a constant rate of 2m3 per minutes. How long will it take to fill the take completely with water.

2) A cuboid has a square face of area 64 cm2. The ratio of its breadth to its length is 2:5. When the cuboid is placed into the tank, 40 cm by 25 cm by 20 cm, the water level reaches the 12 cm mark. Calculate, in litres, the volume of water in the tank? Pls write down the method! :?:

[Winx5015]

:thankyou: tianzhu

[tianzhu]

Winx5015:

:thankyou: tianzhu

Hi

You're welcome.

Best wishes

[tianzhu]

Michaelia0816:

Pls help me with the following question, Tianzhu! 1) A rectangular tank, 1/3 filled with water, has a square base of 4m2. The ratio of its height to its length is 3:5. A tap is turned on and water flows into the tank at a constant rate of 2m3 per minutes. How long will it take to fill the take completely with water.

2) A cuboid has a square face of area 64 cm2. The ratio of its breadth to its length is 2:5. When the cuboid is placed into the tank, 40 cm by 25 cm by 20 cm, the water level reaches the 12 cm mark. Calculate, in litres, the volume of water in the tank? Pls write down the method! :?:

Hi

Q1)Square base ------- 4 sqm

Length (breadth) ----- 2m

height: length ------- 3:5 ------- 1.2:2

The tank is 1/3 filled with water.

Additional volume of water required -------4*0.8 ------ 3.2 cubic m

2 cubic m ------ 1 min

3.2 cubic m ------ 1.6 min

For Q2, please check with your school teacher if volume of solid in displacement of volume is in the syllabus.

Breadth of cuboid ------- 8

Breadth:length ------- 2:5 ------- 8:20

Volume of cuboid ------- 64*20 ------- 1280 cubic cm

Volume of water + cuboid in tank ------- 40*25*12 ------- 12000 cubic cm

Volume of water in tank ------- 12000 – 1280 ----- 10720 cubic cm ------ 10.72 l

Best wishes

[Michaelia0816]

Thank you for your help, Tianzhu! :thankyou:

[thinkgmama]

Hi,

Kindly help with this qn from my daughter’s worksheet.

1) The number of stamps that Mary and Henry had at first was in the ratio 3:1. After Mary bought 56 stamps and Henry sold 15 stamps, Mary then had 6 times as many stamps as Henry. How many stamps did Henry have at first?

2) Ali and Ben shared a sum of money in the ratio of 1:4. If Ali gives Ben $36, Ben will have 6 times as much money as Ali. How much money does Ben have?

[Bunny27]

thinkgmama:

Hi,

Kindly help with this qn from my daughter's worksheet.

1) The number of stamps that Mary and Henry had at first was in the ratio 3:1. After Mary bought 56 stamps and Henry sold 15 stamps, Mary then had 6 times as many stamps as Henry. How many stamps did Henry have at first?

2) Ali and Ben shared a sum of money in the ratio of 1:4. If Ali gives Ben $36, Ben will have 6 times as much money as Ali. How much money does Ben have?

Hi, pls help on this question :

Janice's monthly income is $300 more than Betty's but their monthly expenditures are the same. Over a period of time, Janice saved $1700 while Betty only saved $500.

a) How long does each of them take to save the given amount of money?

b) Given that each of them $1500 per month, what is Janice's monthly income?

Thanks ...

[tianzhu]

Bunny27:

Hi, pls help on this question :

Janice's monthly income is $300 more than Betty's but their monthly expenditures are the same. Over a period of time, Janice saved $1700 while Betty only saved $500.

a) How long does each of them take to save the given amount of money?

b) Given that each of them $1500 per month, what is Janice's monthly income?

Thanks ...

Hi

Good morning.

Janice saved $1700 while Betty only saved $500.

1700 – 500 ------ 1200

Janice's monthly income is $300 more than Betty's

1200/300 ------- 4

They took 4 months.

b)

I think there is some missing word in the highlighted phrase.

Given that each of them spends $1500 per month.

1700/4 ------ 425

Janice’s monthly salary ------ 1500 + 425 ----- 1925

Best wishes

[tianzhu]

thinkgmama:

Hi,

Kindly help with this qn from my daughter's worksheet.

1) The number of stamps that Mary and Henry had at first was in the ratio 3:1. After Mary bought 56 stamps and Henry sold 15 stamps, Mary then had 6 times as many stamps as Henry. How many stamps did Henry have at first?

2) Ali and Ben shared a sum of money in the ratio of 1:4. If Ali gives Ben $36, Ben will have 6 times as much money as Ali. How much money does Ben have?

Hi

Good Morning.

For Q2, you may use MD or UM.

At first
Ali:Ben - ------ 1:4 (5) ------- 7:28 (35)

Change
Ali:Ben ------- -36:+36

In the end
Ali:Ben - ------ 1 :6 (7) ------- 5:30 (35)

The amount of money remains the same before and after.
Make the total number of units the same.

2 units ------ 36
1 unit ------ 18

Ben ------ 28*18 ------ 504

For Q1, please check your question.

I’ve found a similar question to yours, some numbers are different.

If the question is revised as shown, then you may use “Units and Parts’ to solve it.

The number of stamps that Mary and Henry had at first was in the ratio 3 : 1. After Mary bought 36 stamps and Henry sold 20 stamps, Mary then had 5 times as many stamps as Henry. How many stamps did Henry have at first?

At first
Mary’s stamps : Henry’s stamps ----- 3 units:1 unit

Change
Mary’s stamps : Henry’s stamps ----- +36: -20

In the end
Mary’s stamps : Henry’s stamps ----- 5 parts:1 part

3 units + 36 ------ 5 parts

1 unit – 20 ------ 1 part
(x5)
5 units – 100 ------ 5 parts

Equalise the parts or cross multiply.

3 units + 36 ------ 5 units – 100
2 units ------ 136
1 unit ------ 68

Henry ------ 68 stamps (at first)

Now, try to do your question, change 56 to 66.

Best wishes