Q&A - PSLE Math

[tianzhu]

Essential:

Hi Tianzhu , I am to trouble you again.

12) Four children Min, Nat, Tom and Caleb each have savings. The amount of money Nat has is 1/3 of the total amount of money Tom , Min and Caleb have. The amount of money Tom has is 1/4 of the total amount of money Nat , Min And Caleb have. The amount of money Min has is 1/5 of the total amount of Nat. Tom and Caleb have. If Caleb saves $1035 . How much do the four children have altogether?

Hi

The total amount of money in the three scenarios is the same. Make the total number of units the same.

A common multiple of 4, 5 and 6 is 60.

Nat : (Tom + Min + Caleb) ------ 1:3 ((4) ------ 15:45 (60)
Tom : (Nat + Min + Caleb) ------ 1:4 (5) ------ 12:48 (60)
Min : (Nat + Tom + Caleb) ------ 1:5 (6) ------ 10:50 (60)

Nat ------ 15 units
Tom ------ 12 units
Min ------- 10 units
Caleb ------ 23 units

23 units ------ 1035
1 unit ------ 45

60*45 ------ 2700

Best wishes

[tianzhu]

Winx5015:

Hi please help me with the following questions.


(1). A taxi and a lorry were travelling along the same road at a uniform speed of 80km/h and 56km/h respectively. At 10.45am, the lorry was 30km ahead of the taxi. 45 min later, the lorry broke down.
(a). How far away was the taxi from the lorry when the lorry broke down?
(b). At what time would the taxi pass the broken-down lorry?

Thanks

Hi

As in any Speed question, it’s always useful to have a simple representation.

Distance travelled by lorry@45mins ----- 56*3/4 ------ 42km

Distance travelled by taxi@45mins ------ 80*3/4 ------ 60km

The lorry broke down at 11.30am

30 + 42 ------ 72

72 – 60 ----- 12

The taxi was 12km away when the lorry broke down.

12/80*60 ------ 9

The taxi passed the broken down lorry at 11.39 am

Best wishes

[YumYum]

Hi, can anyone pls help with this Qn?


A bus was scheduled to travel from Town X to Town Yat a fixed speed, V km/h.
If the speed of the bus was increased by 20%, it could arrive at Town Y 80 minutes ahead of schedule. Instead, if the bus travelled the first 275 km at V km/h and after that it increased the speed by 25%, it could reach Town Y 30 mins ahead of schedule. Find the dustance between the 2 towns.

thanks!

[tianzhu]

Winx5015:

Hi please help me with the following questions.


(2). At 6pm, May and Sue started jogging from their homes towards each other. May jogged at an average speed of 40m/min while Sue jogged at an average speed of 80m/min. After some time, both girls met at a park which was 400m from the midpoint of the distance between the two houses.
(a). Find the total distance covered by May and Sue.
(b). At what time did they meet at the park? (Express your answer using the 24-h clock)
Thanks

Hi

One way to do this question is use the concept that the distance travelled at a given period of time is in direct proportion to the speed.

May:Sue ------ 40:80 ------ 1:2 (speed ratio)
May:Sue ------ 1:2 (distance ratio)

To avoid working with decimals, I’ll use an equivalent ratio of 2:4

When they met, May travelled 2 units and Sue travelled 4 units.

The mid point is at 3 units

1 unit ------ 400
6 units ------ 400*6 ------ 2400m (total distance covered by May and Sue).

800/40 ------ 20

They met after running for 20 mins

The time was 1820h

Best wishes

[tianzhu]

Winx5015:

(3). Peter and Tom shared a number of books in the ratio of 3:4. After Peter and Tom bought another 19 books and 2 books respectively, the ratio becomes 4:3. How many books did Peter have at first? (Using External Transfer Concept)

Thanks

Hi

You may use “Units and Parts”

At first
Peter: Tom ------ 3 units:4 units

Change
Peter: Tom ------ 19:2

In the end
Peter: Tom ------ 4 parts: 3 parts

Equalise the parts or cross multiply.

3 units + 19 ------ 4 parts
(x3)
9 units + 57 ------ 12 parts

4 unit + 2 ------- 3 parts
(x4)
16 units + 8 ------ 12 parts

9 units + 57 ------- 16 units + 8
7 units ------ 49
1 unit ------ 7

Peter ------ 3*7 ------- 21

Best wishes

[Ngserene617]

tianzhu:

Winx5015:

(3). Peter and Tom shared a number of books in the ratio of 3:4. After Peter and Tom bought another 19 books and 2 books respectively, the ratio becomes 4:3. How many books did Peter have at first? (Using External Transfer Concept)

Thanks

Hi

You may use “Units and Parts”

At first
Peter: Tom ------ 3 units:4 units

Change
Peter: Tom ------ 19:2

In the end
Peter: Tom ------ 4 parts: 3 parts

Equalise the parts or cross multiply.

3 units + 19 ------ 4 parts
(x3)
9 units + 57 ------ 12 parts

4 unit + 2 ------- 3 parts
(x4)
16 units + 8 ------ 12 parts

9 units + 57 ------- 16 units + 8
7 units ------ 49
1 unit ------ 7

Peter ------ 3*7 ------- 21

Best wishes

Hi, I need help on this question:

1. When a tank is 1/3 filled with water. It weighs 58kg. If it is 3／4 filled with water, it weighs 108kg.
a) What is the weight of the empty tank?
b) What is the weight of the tank when it is completely filled with water?

Thanks...

[Winx5015]

tianzhu,


Really appreciate your help

[tianzhu]

YumYum:

Hi, can anyone pls help with this Qn?


A bus was scheduled to travel from Town X to Town Yat a fixed speed, V km/h.
If the speed of the bus was increased by 20%, it could arrive at Town Y 80 minutes ahead of schedule. Instead, if the bus travelled the first 275 km at V km/h and after that it increased the speed by 25%, it could reach Town Y 30 mins ahead of schedule. Find the dustance between the 2 towns.

thanks!

Hi

The answer is 400km.

This is definitely not a PSLE type of Speed question.

Where is this question from?

Best wishes

[Chan09]

Hi, need some help on this:

Area of triangle is 1/3 the area of the square. After the shaded area is removed, the unshaded area of the square becomes 4 times the unshaded area of the triangle. Given that the unshaded area is 81cm2, find the length of the square?

The picture for this question shows a triangle and square with the square overlapping one corner of the triangle.
Ans: 27cm

Thank u.

[YumYum]

Hi Tianzhu,


the Qn is adapted from a math Olympiad Qn given to students in the school MO class. Not sure if this is the right forum to post this as I thought it’s related to speed but wasn’t aware that it’s not in PSLE syllabus…

Do you mind explaining how the answer is derived?

Thanks!

Thanks