Q&A - PSLE Math

[James Ang]

Came across some thinking type questions in sec 1 textbooks that can be solved using model/primary methods.;


1. 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?


2. Two candles of the same height are lit at the same time. The first candle takes 5h to burn completely. The second candle takes 4h to burn completely. If each candle burns at a constant rate, how long does it take, in hours, for the height of the first candle to be four times that of the second candle?

[leesf]

Hi, would appreciate help on the following questions. Thanks


St Nicholas 2009 Prelim :
At carpark P, the number of lorries to that of vans was in the ratio 3:7. At carpark Q, the number of lorries to that of vans was in the ratio 8:9. When 40% more lorries from an industrial park entered carpark P, and 20% of the vans at carpark Q moved to carpark P, there were 76 fewer lorries at carpark P than at carpark Q. How many vehicles were there altogether at the two carparks finally?

Nanyang 2009 SA1
Audrey and Belle have some money each. If Audrey spends $18 and Belle spends $24 each day, Audrey will still have $25 left when Belle has spent all her money. If Audrey spends $13 and Belle spends $30 each day, Audrey will still have $139 left when Belle has spend all her money. How much money do they have altogether?

[Muffins]

For the St. Nicholas Question, the answers are on this website: http://www.thinkingmath.com.sg/forum/35-thinkingmathonsponge/950-real-hard-ratio.html, http://www.kiasuparents.com/kiasu/forum/viewtopic.php?t=280&postdays=0&postorder=asc&start=900


Carpark P
L : V
3 : 7
= 15 : 35
Carpark Q
L : V
8 : 9
= 40 : 45

15u X 140% = 21u
40u - 21u = 19u which is 76
21u + 35u + 40u + 45u = 141u
76/19 = 4
4 X 141 = 564

[tianzhu]

Hi


In answering this question, it’s important to note that the amount of money in either cases or scenarios remains the same. The question involves a double if, and the key to unlock it is to recognise that Audrey and Belle have the same amount of money in either cases/scenarios.

You can either use MD or Units Method to solve such questions.With the help of equivalent ratios, I’ll be using Units Method in this post.

Hope this helps

Best wishes

http://farm5.static.flickr.com/4118/4899664180_c55b84423d_b.jpg\">

[leesf]

Hi Muffins & Tianzhu,


Thanks for your illustrations. It really helps.

[leesf]

Hi Muffins,


Can you explain why you multiply the ratio by 5 and not any other numbers? I looked back the preious link but still clueless. Thanks

[tianzhu]

Hi


The first candle takes a longer time to burn completely as compared to the second candle. Logically speaking, it should be fatter or has a bigger diameter. I feel a good way to tackle this question is to use MD.Alternatively, you may also work it out using Units Method.

You can have more practice by doing this problem.

P5 maths question:

Two candles of the same height are lit at the same time. The first is consumed in 4 hours, the second in 3 hours. Assuming that each candle burns at a constant rate, how many hours after being lit was the height of the first candle twice the height of the second?

Hope this helps.

Best wishes

http://farm5.static.flickr.com/4138/4900948596_beab67f0bc_b.jpg\">

[tianzhu]

leesf:

Hi Muffins & Tianzhu,


Thanks for your illustrations. It really helps.

Hi

You're welcome.

Best wishes

[Yu Xuan]

[quote="tianzhu"]Hi



Two candles of the same height are lit at the same time. The first is consumed in 4 hours, the second in 3 hours. Assuming that each candle burns at a constant rate, how many hours after being lit was the height of the first candle twice the height of the second?

[quote]

Hi Tianzhu

From the model, DS wonder since it is drawn in accordance to the first candle’s 5 hrs, then the working can be such instead;

3p * 5 = 15p
20 p ==> 5h
Length of candle ==> 4p * 5 = 20p
15p ==> 5 * 15/20 = 3 3/4h

Logically, both 15/20 are 12/16 are equivalent fractions so it should be accepted right?

Thank you for your time.

Yu Xuan

15p ==>

[tianzhu]

leesf:

Hi Muffins,


Can you explain why you multiply the ratio by 5 and not any other numbers? I looked back the preious link but still clueless. Thanks

Hi

A ratio is used to compare two or more quantities with the same units.
Questions on Ratios can be overwhelming at times, especially when we are trying to interpret the context of the question.

In this question, what Muffins did was to assume that

(1)40% more lorries are added to the existing number of lorries in Car park P

(2)The unit of measure for the before and after ratios are of the same value.

Muffins multiplied the original ratios by 5 so to avoid decimals in the calculations. You may use other factors as long as all ratios are multiplied by the same number. You’ll still get the same answer, but may end up working with decimals.

Another way to do this question is to use systematic listing/tabulated list.

Best wishes