Q&A - PSLE Math

[tianzhu]

Maths Monster:

Hi,

No. The sum D1 + D2 + D3 will be different if the average speed of the uphill and downhill is not equal to ground level speed. For illustration purpose, say D1 = D2 and the equation is

D1 + D2 + 2D3 = 10

D1 or D2 = 0, D3 = 5 and Total = 5
D1 or D2 = 1, D3 = 4 and Total = 6
D1 or D2 = 2, D3 = 3 and Total = 7
D1 or D2 = 3, D3 = 2 and Total = 8
and so on....

There are multiple answers for D1, D2 and D3 and they add up to give the different answers.

D1 + D2 + D3 will give one answer if the average of the uphill and downhill is equal to the ground level speed.

Hi

D1 + D2 + 2D3 = 10

Please explain how you arrive at D1=D2(not indicated in question) and 2D3.

(D1 - Uphill, D2 - Downhill, D3 - Ground level)

Best wishes

[Maths Monster]

tianzhu:

Maths Monster:

Hi,

No. The sum D1 + D2 + D3 will be different if the average speed of the uphill and downhill is not equal to ground level speed. For illustration purpose, say D1 = D2 and the equation is

D1 + D2 + 2D3 = 10

D1 or D2 = 0, D3 = 5 and Total = 5
D1 or D2 = 1, D3 = 4 and Total = 6
D1 or D2 = 2, D3 = 3 and Total = 7
D1 or D2 = 3, D3 = 2 and Total = 8
and so on....

There are multiple answers for D1, D2 and D3 and they add up to give the different answers.

D1 + D2 + D3 will give one answer if the average of the uphill and downhill is equal to the ground level speed.

Hi

D1 + D2 + 2D3 = 10

Please explain how you arrive at D1=D2(not indicated in question) and 2D3.

(D1 - Uphill, D2 - Downhill, D3 - Ground level)

Best wishes

Hi,

What I was trying to show is that if the constants for each of the variables are different, the equation cannot be simplified to a form of D1+D2+D3 and hence solve for the total.

Apologize for not making this clear in the illustration

Let use back the previous example.

Downhill: 72 km/h
Ground level: 63 km/h
Uphill: 56 km/h
The equation derived is 2/63 D1 + 2/63 D2 + 2/63 D3 =26/3
which the constant is the same for D1, D2 and D3, hence it can be simplified to D1+D2+D3 form and it can be easily solved.

To illustrate my point that there are multiply solutions if the average of the uphill and downhill is different as the ground speed, let assume that the ground speed is 64 km/h,. The equation will be 2/63 D1 + 2/63 D2 + 2/64 D3 =26/3
The constants are different and it cannot be simplified to the D1+D2+D3 form. As this is a 3 variables in a single equation, there are infinite solutions for D1, D2 and D3 and also the total. Hope this is clear. Pm me if you need further clarification.

[tianzhu]

Q1)Jack cycles to his friend's house and then returns home by the same route. He always cycles at 4 km/h when going uphill and, 12 km/h when going downhill, and 6 km/h when on level ground. If his total cycling time is 2h 20mins, what is the distance he cycles in km?


Q2) Downhill: 72 km/h
Ground level: 63 km/h
Uphill: 56 km/h
Car travels from Town A to Town B in 4 hours. It returns to Town A using the same route in 4 h 40 min. What is the distance between Town A and Town B?

Hi

Other than using algebra, this is another way to tackle these questions.

There are three types of terrains, uphill, downhill and level ground.
The point to note is if the cyclist moves uphill in one direction, on the way back he moves downhill. So what is the average speed for this part of the road?

Use common multiple to find the average speed. Then use the formula, Distance -----Speed*Time

Hope this helps.

Best wishes

http://farm5.static.flickr.com/4118/4944165296_9917ee7199_b.jpg\">

[tianzhu]

verykiasu2010:

just hijack the topic for one post : if only the singaporean population multiplies like the hamster!

Hi

The population is rising.

S'pore population at 5.08m.
http://www.straitstimes.com/BreakingNews/Singapore/Story/STIStory_573395.html

Best wishes

[capricorn28]

Hi, the following are P5 maths questions. Hope somebody can help us on these.


1) After counting, Nessie found that 0.4 of the flowers in her garden are roses and 3/4 of the remaining flowers are tulips. The rest of the flowers are daisies. She has 30 more tulips than roses. How many daisies are there in the garden?

2) Denver would be 43 years old in a few years time. He would be 33.5 years old in half that time. He is 5 times his son’s age. How old is his son?

3) Mr Yap bought 4kg of durians and 3kg of apples for $50. If he bought 3kg of durians and 4kg of apples, he would pay $2 less. What is the cost of 1kg of durian?

4) The cost of tickets to the underwater world in Sentosa for 2 Adults and 3 Children is $92. The cost of 6 Adults and 4 Children is $196. What is the cost if Mr Tan goes with his wife and his 5 children?

Thank you.

[tianzhu]

After counting, Nessie found that 0.4 of the flowers in her garden are roses and 3/4 of the remaining flowers are tulips. The rest of the flowers are daisies. She has 30 more tulips than roses. How many daisies are there in the garden?


Hi

This question touches on Remainder concept or Part whole concept.
Using equivalent ratios, change 4:6 to 8:12.You may draw a MD or use the Branch method.

9units ---tulips
8 units ----roses
3 units ----daisies
1 unit ---- 30
3 units ----90

Mr Yap bought 4kg of durians and 3kg of apples for $50. If he bought 3kg of durians and 4kg of apples, he would pay $2 less. What is the cost of 1kg of durian?

Hi
DDDD AAA -------50
DDD AAAA ------48

D costs $2 more than A

4kg of durians and 3kg of apples for $50.

AAAA + 8 +3A ------ 50
A -------6
D ------8

You may draw MD with 1 bigger rectangle to show 1kg of durians and 1 smaller rectangle to show 1 kg of apples. Or you may choose to work with letters(alphabet) A and D to represent 1kg of apples and 1 kg of durians respectively once you become more familiar with such questions.

Best wishes

[tianzhu]

The cost of tickets to the underwater world in Sentosa for 2 Adults and 3 Children is $92. The cost of 6 Adults and 4 Children is $196. What is the cost if Mr Tan goes with his wife and his 5 children?


Hi

Q4 is similar to Q2.Once again, you may choose to work with MD or letters(alphabet), in this case A and C to represent adults and children.

AA CCC ----- 92
AAAAAA CCCC ------196

AAA CC ------98 (196/2)

A costs $6 more than C

CC +12+CCC ------92
C -------16
A ------22

AA ------44
CCCCC ------ 80
Total cost -------- 124

Best wishes

[tianzhu]

Denver would be 43 years old in a few years time. He would be 33.5 years old in half that time. He is 5 times his son's age. How old is his son?


Hi

I am not too sure if I've interpreted this question correctly.

1) Draw a rectangle block to represent present age of Denver

2) Add another rectangle block to (1) to show extension to 43 years old.

3) Draw same rectangle block as (1).Draw half the size of rectangle block as(2) to show future age of 33.5.

4) 43-33.5 ---9.5

5) Denver’s present age is 24.

Therefore his son is 24/5 ----4.8 years old. (Decimals still possible for age can be in years, months and days)

Check
Denver is now 24 years old.
19 years from now, he’ll be 43 years old.
In half of 19 years (9.5), he’ll be 33.5 years old

Please help to check calculations for these four questions as solutions done in a rush.

Best wishes

[capricorn28]

Hi tianzhu


Thank you for the quick and clear reply.
Have a good day.

[tianzhu]

capricorn28:

Hi tianzhu


Thank you for the quick and clear reply.
Have a good day.

Hi

You're welcome.

Best wishes