Q&A - PSLE Math

[MathIzzzFun]

Xiao Hu:

MathIzzzFun:

[quote=\"Michaelia0816\"]Guys, I was teaching my cousin maths and I came across this speed question. I couldn't believe it, that I couldn't solve! Even the answer keys are a mystery to me! :? :? :?


Singapore Hokkien Hway Kuan P6 Math 2011 Qn 15

A car left Town A for Town B. At the same time, a lorry left Town B for Town A. The average speed of the car was 90km/h while the speed of the lorry was 70km/h. The two vehicles passed each other at a point 36km away from the mid-point between Town A and Town B.
What was the distance between Town A and Town B?

with many thanks and cheers

Solutions:
http://singaporemathproblems.com/uploads/3/0/9/8/3098498/answer__p6-008.pdf

This is not I created page, I just helping to find the answer, pls read the note of that web, the answer key is wrong!

please note that the posted answer at provided link is incorrect.
Midpoint --> 8/16 AB
So, 8/16-7/16 = 36km, 1/16--> 36km,
Total distance betweeen AB=16 x36 = 576 km

cheers.

Hi MathIzzzFun,
Agreed with you that the link's answer is not correct. But may I ask about your approach? I hope you would be kind enough to share how you come to use 8/16 AB? What is the concept behind to using the denominator 16 and then a fraction of 8/16AB?

Thanks in advance for sharing,
Xiaohu.[/quote]using speed ratio--> car's speed : lorry's speed = 90:70 = 9u : 7u
This means that in the same time,
car travel 9u & lorry travel 7u.
when they meet,
distance travelled by car --> 9u
distance travelled by lorry --> 7u
Total distance between AB = 9u+7u=16u
Midpoint of AB = 16u / 2 = 8u
So, 9u - 8u = 36 km

cheers.

[whitety]

Hi, need help on these 2 qns.


1) George and Hamid drove at constant speeds from City A to City B. They started their journey at the same time. When George completed 3/4 of the journey, Hamid was 18km behind George. George reached City B 20min before Hamid. Find Hamid’s speed in km/h.

2) in a bag, the ratio of the number of $2 notes to the number of $10 notes was 2:5. Ten $10 notes were removed from the bag to exchange for $2 notes which were then put back into the bag. The total value of money in the bag was unchanged after the exchange. The ratio of the number of $2 notes to the number of $10 notes then became 11:5. What was the difference between the value of the $10 notes and $2 notes after the exchange?

Thanks!

[MathIzzzFun]

whitety:

Hi, need help on these 2 qns.


1) George and Hamid drove at constant speeds from City A to City B. They started their journey at the same time. When George completed 3/4 of the journey, Hamid was 18km behind George. George reached City B 20min before Hamid. Find Hamid's speed in km/h.

2) in a bag, the ratio of the number of $2 notes to the number of $10 notes was 2:5. Ten $10 notes were removed from the bag to exchange for $2 notes which were then put back into the bag. The total value of money in the bag was unchanged after the exchange. The ratio of the number of $2 notes to the number of $10 notes then became 11:5. What was the difference between the value of the $10 notes and $2 notes after the exchange?

Thanks!

1) George completed 3/4 of journey, Hamid 18km behind
So, when George completed the journey (4/4), Hamid will be 24km behind
Hamid's speed = 24km/20 x 60 km/h = 72 km/h

2) 10 x $10 = 50 x $2
At first, number of $2 notes: $10 notes --> 2u : 5u
In the end, number of $2 notes: $10 notes --> 2u+50 : 5u-10 = 11 : 5

cross multiply/equalize:
10u + 250 = 55u - 110
1u --> 8 .. can you continue from here ?

difference in value = $168 ($10 --> $300, $2--> $132)

cheers.

[Xiao Hu]

[quote="MathIzzzFun

using speed ratio–> car’s speed : lorry’s speed = 90:70 = 9u : 7u
This means that in the same time,
car travel 9u & lorry travel 7u.
when they meet,
distance travelled by car –> 9u
distance travelled by lorry –> 7u
Total distance between AB = 9u+7u=16u
Midpoint of AB = 16u / 2 = 8u
So, 9u - 8u = 36 km

cheers.[/quote]

Hi MathIzzzFun,
Perfect !! Thanks so much. I did not even begin to think about using ratio and then what you reduced them to 9u and 7u.

Have a good weekend,
Xiaohu.

[Chan09]

Need help on these; thank you


1) team A and team B sent pupils in groups of 10, for a ball game. If the 2 teams used mini vans that have a seating capacity of 14 passengers, they will need 72 vans. If they use mini vans that have a seating capacity of 19, team B will need 7 more vans than team A. If the 2 teams do not share a van and each van is pack to a max of 19 for team B, how many more pupils are there in team B than team A?
Ans: 140

2) There are 98 teachers and each female teacher has 8 notepads and each male teacher has 3 notepads given to them. The male teachers received 355 notepads less than the female teachers. How many female teachers are there?
Ans: 59, for this question I applied the excess and shortage concept though I understand that this is incorrect as it is suppose to make a supposition. Plse help.

[fightingmom]

Hi,


Please help with the following question:

Miss Koh had 130 apples and oranges. After she sold 2/3 of the apples and 2/5 of the oranges, she had 36 more oranges than apples left. How many fruits had she left ?

TIA!

[fightingmom]

Hi,


Sorry can also help with another question?

There are some chairs in a hall. 1/2 of them are put in short rows and 2/5 of them are placed in long rows. The remaining chairs are placed at the back of the hall. There are 20 short rows and 6 long rows. Each long row has 20 more chairs than each short rows. How many chairs are there in all ?

TIA!


I worked out and my answer is 208 … Doesn’t seem right though …

[MathIzzzFun]

fightingmom:

Hi,


Please help with the following question:

Miss Koh had 130 apples and oranges. After she sold 2/3 of the apples and 2/5 of the oranges, she had 36 more oranges than apples left. How many fruits had she left ?

TIA!

After sales of 2/3 of apples & 2/5 of oranges, number of apples and oranges remaining:
Apples (1/3) --> 3 units
Oranges (3/5) --> 3 units + 36 = 3 x (1 unit + 12)

At first,
Apples --> 9 units
Oranges --> 5 units + 60
Total --> 14 units + 60 = 130
1 unit --> 5

Number of fruits left:
Apple --> 15
Oranges --> 51
Total --> 66

cheers.

[MathIzzzFun]

fightingmom:

Hi,


Sorry can also help with another question?

There are some chairs in a hall. 1/2 of them are put in short rows and 2/5 of them are placed in long rows. The remaining chairs are placed at the back of the hall. There are 20 short rows and 6 long rows. Each long row has 20 more chairs than each short rows. How many chairs are there in all ?

TIA!


I worked out and my answer is 208 ... Doesn't seem right though ....

Ratio of chairs in short rows : long rows : back of hall = 1/2 : 2/5 : 1-1/2-2/5 = 5 : 4 : 1--> 20u : 16u : 4u --- total 40u

For long rows,
16u = 6u + 6 x 20
1u --> 12
Total number of chairs --> 40 x 12 = 480

cheers.

[speedmaths.012624com]

fightingmom:

Hi,


Please help with the following question:

Miss Koh had 130 apples and oranges. After she sold 2/3 of the apples and 2/5 of the oranges, she had 36 more oranges than apples left. How many fruits had she left ?

TIA!

Hi,

One possible method:
Using the Advanced Model Method
(or Bags and Boxes Method)

Look at the 2 denominators; 3 and 5.

Let Miss Koh put the apples in 3 Bags.
Let Miss Koh put the oranges in 5 Boxes.

Miss Koh had 130 apples and oranges
3 Bags and 5 Boxes contain 130 fruits.
3 Bags + 5 Boxes → 130 fruits
3 Bags → 130 fruits - 5 Boxes .............. (Row 1)

She sold 2/3 of the apples and 2/5 of the oranges
She sold 2 Bags and 2 Boxes of fruits.
She had 1 Bag and 3 Boxes of fruits left.

She had 36 more oranges than apples left.
1 Bag + 36 fruits → 3 Boxes
1 Bag → 3 Boxes - 36 fruits
(x 3)
3 Bags → 9 Boxes - 108 fruits......................(Row 2)

3 Bags = 3 Bags
Row 2 = Row 1
3 Bags → 9 Boxes - 108 fruits → 130 fruits - 5 Boxes

9 Boxes - 108 fruits → 130 fruits - 5 Boxes

Add 5 Boxes to both sides of the equation
14 Boxes - 108 fruits → 130 fruits - 0 Box

Add 108 fruits to both sides of the equation
14 Boxes - 0 fruit → 238 fruits - 0 Box

14 Boxes → 238 fruits
1 Box → 17 fruits
3 Boxes → 51 fruits

(From above)
1 Bag → 3 Boxes - 36 fruits
1 Bag → 51 fruits - 36 fruits = 15 fruits

She had 1 Bag and 3 Boxes of fruits left

She had 15 fruits + 51 fruits = 66 fruits left

Hope this helps.

Cheers

speedmaths.com

PS.
Parents who wish to know more about the Advanced Model Method can check out our thread in the Happenings forum.

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