Q&A - PSLE Math

[tianzhu]

its888me:

Kingsley planned to cycle from Town P to Town Q. If he were to cycle at 10 km/h, he would reach Town Q at 7.45pm. If he were to cycle at 12 km/h, he would reach Town Q at 7.15pm. What was the distance between Town P and Town Q?

Hi

You may tackle this question in a few ways.

For Speed questions, it’s helpful to start with a simple diagram.

At 12 km/h, he would reach Town Q at 7.15pm.

If he were to cycle at 10 km/h, he would be (10*1/2) or 5 km away.

Difference in speed ------- 12 – 10 ------ 2

Time taken ------- 5/2 ------- 2.5 h

Distance between P and Q ------- 2.5*12 ------- 30 km

or alternatively (3*10) ------- 30 km.

Another way if students are familiar with inverse proportion.

Speed is inversely proportional to time (distance remains constant).When speed is higher, time taken is shorter.

Speed -------- 12:10 ------- 6:5

Time ------- 5:6

1 unit ------- 1/2h

5 units ------- 5*1/2 ------- 2.5

Distance between P and Q -------- 2.5*12 ------- 30 km

Another way, use common multiple.

A common multiple of 12 and 10 is 60.

Distance ------- Speed*Time

60/12 ------ 5h

60/10 ------ 6h

Difference -------- 1h

We want a difference of 1/2h, so reduce distance to 30km.

30/12 ------- 2.5h

30/10 -------- 3h

Difference ------- 0.5h or 1/2h

Best wishes

[tianzhu]

its888me:

TGhere were some blue marbles and white marbles in a bag. If 70 blue marbles were to be removed from the bag, the ratio of the number of blue marbles to the number of white marbles would be 3 : 4. If 112 white marbles were to be removed from the bag instead, the tatio of the number of blue marbles to the number of white marbles would be 8 : 7. When 48 more blue marbles were to be added into the bag, what percentage of all the marbles would be blue marbles?

Hi

You may use \"Units and Parts\".

Due to time constraint, I am unable to present in slide but will give some pointers.

If 70 blue marbles were to be removed from the bag, the ratio of the number of blue marbles to the number of white marbles would be 3 : 4.

At first

Blue ------- 3u + 70

White ------- 4u

In the end

Blue ------- 3u

White ------- 4u

If 112 white marbles were to be removed from the bag instead, the ratio of the number of blue marbles to the number of white marbles would be 8 : 7.

At first

Blue ------- 3u + 70

White ------- 4u

In the end

Blue ------- 8p

White ------- 7p

Equalising the parts or cross multiply.

3u + 70 ------- 8p

4u – 112 ------- 7p

21u + 490 ------- 32u – 896

11u -------- 1386

1 u ------- 126

Number of blue marbles -------- 3*126 + 70 ------- 448

Number of white marbles -------- 4*126 ------- 504

When 48 more blue marbles were to be added into the bag.

448+48/(448+48+504)*100% -------- 49.6%

Best wishes

[underthesea]

tianzhu:

underthesea:

This is dd's prelim question.


Mrs B used either 4 red buttons or 2 blue buttons to make each dress. The total number of dresses she made was 35. The total number of red buttons used was 74 more than the total number of red buttons used.

(a) how many red buttons were used altogether?
(b) how many blue buttons were used altogether?

Besides guess & check, any other method to solve this problem?

TIA.

Hi

Please check sentence highlighted in pink.

Sorry for the mistake. Thank you TianZhu for the solution. :thankyou:

[anneshirleygilbert]

Good morning.


I need some help to calculate average speed.

Let’s say, Jack travelled 300 km from Town P to Town Q. He started his journey at 7.00 and reached his Town Q at 1.00. In between, he took a break from 9.00 to 10.00am. When we calculate average speed, do we divide 300km by 6 hrs (total time taken) or 300km divided by 5 hrs (actual travelling time)?

In other words, do we include that hour of break (9.00 to 10.00) into the total time taken?

My daughter and I differed in our interpretation.

[tianzhu]

anneshirleygilbert:

In other words, do we include that hour of break (9.00 to 10.00) into the total time taken?


My daughter and I differed in our interpretation.

Hi

I suggest you check with the school teachers whether questions with rest periods are included in the PSLE syllabus.

When we are talking about the whole journey, we have to take into account the rest time.

Take for example,

Jack travelled for 1 h from Town A to Town B at a speed of 60km/h. He rested in Town B for 10 min. After that, he continued travelling for 20 min to Town C at a speed of 45km/h. Find his average speed for the whole journey.

Best wishes

[Zhu99]

anneshirleygilbert:

Good morning.


I need some help to calculate average speed.

Let's say, Jack travelled 300 km from Town P to Town Q. He started his journey at 7.00 and reached his Town Q at 1.00. In between, he took a break from 9.00 to 10.00am. When we calculate average speed, do we divide 300km by 6 hrs (total time taken) or 300km divided by 5 hrs (actual travelling time)?

In other words, do we include that hour of break (9.00 to 10.00) into the total time taken?


My daughter and I differed in our interpretation.

Average speed = Total Distance / Total Time.

Total Time is from Start to End of Journey, inclusive of rest time.

[its888me]

its888me:

its888me:

Need help in 2 Questions, Nanyang Prelim 2010, Paper 2:


Q10:

Kingsley planned to cycle from Town P to Town Q. If he were to cycle at 10 km/h, he would reach Town Q at 7.45pm. If he were to cycle at 12 km/h, he would reach Town Q at 7.15pm. What was the distance between Town P and Town Q?

Q17:

TGhere were some blue marbles and white marbles in a bag. If 70 blue marbles were to be removed from the bag, the ratio of the number of blue marbles to the number of white marbles would be 3 : 4. If 112 white marbles were to be removed from the bag instead, the tatio of the number of blue marbles to the number of white marbles would be 8 : 7. When 48 more blue marbles were to be added into the bag, what percentage of all the marbles would be blue marbles?


TIA!

Can someone help me with the 2 questions? Many thanks!

[2632parent]

Need help in the following question on speed,


1) Ali and Ben started jogging from Park X to Park Y at the same time. Ali jogged at an average speed of 7.5 km/h while Ben jogged at an average speed of 4.5km/h. After jogging for 1.2h, Ali decided to turn back and jog toward Ben. Ali met Ben at Point Z which was halfway between Park X and Park Y. Ali and Ben then continued their jog together toward Park Y at an average speed of 4.5km/h. What was the distance between Park X and Park Y.

Thank you

[tianzhu]

2632parent:

Need help in the following question on speed,


1) Ali and Ben started jogging from Park X to Park Y at the same time. Ali jogged at an average speed of 7.5 km/h while Ben jogged at an average speed of 4.5km/h. After jogging for 1.2h, Ali decided to turn back and jog toward Ben. Ali met Ben at Point Z which was halfway between Park X and Park Y. Ali and Ben then continued their jog together toward Park Y at an average speed of 4.5km/h. What was the distance between Park X and Park Y.

Thank you

Hi

Good Morning.

As usual for Speed questions, start with a simple diagram.

X at one end, W at the midpoint and Y at the other end.

After jogging 1.2h

Ali ------- 1.2*7.5 ------- 9km

Ben ------- 1.2*4.5 ------- 5.4km

Hence, to the right of W, draw a point A to show the position of Ali.

Also, draw a point B before W to represent the position of Ben.

Distance between Ali and Ben ------- 3.6 km (9-5.4)

In 1h, Ali and Ben covered 12 km (7.5 + 4.5)

Hence, they would covered 3.6 km in 0.3h (3/10)

Distance covered by Ben in 0.3h -------- 4.5*0.3 ------- 1.35

Distance from X to W ------- 1.35 + 5.4 -------- 6.75

Distance between Park X and Park Y ---------- 6.75*2 -------- 13.5km

Alternatively, if students are familiar with inverse proportion, they may also use it to calculate the distance travelled by Ben.

Speed ratio

Ali:Ben ------- 7.5:4.5 -------- 5:3

The distance ratio remains the same as 5:3

Distance covered by Ben --------3/8*3.6 -------- 1.35 km

Best wishes

[2632parent]

Thank you councillor for your early morning reply. Really appreciate your solution, thank you.