Q&A - PSLE Math

[benleetube]

Hi all, everyone. Can you guys help me with this question? I am not sure if this question have been posted before, but here is it:


At 9 a.m., John was cycling from point A to point B. At the same time, Mary was cycling from point B to point A using the same route as John. Cycling at a speed of 4km/h faster than Mary, John would pass Mary 300m away from the midpoint.

(A) what time did they pass each other?

(B) if John took another 3 minutes to reach point B, what time would Mary reach point A?

(Appeared in catholic high SA2(prelim) paper as question 15)

Thanks in advance.

[corneyAmber]

bobsg01:

Many thanks to ksi.


:hi5:

:welcome: :hi5:

[tianzhu]

benleetube:

Hi all, everyone. Can you guys help me with this question? I am not sure if this question have been posted before, but here is it:


At 9 a.m., John was cycling from point A to point B. At the same time, Mary was cycling from point B to point A using the same route as John. Cycling at a speed of 4km/h faster than Mary, John would pass Mary 300m away from the midpoint.

(A) what time did they pass each other?

(B) if John took another 3 minutes to reach point B, what time would Mary reach point A?

(Appeared in catholic high SA2(prelim) paper as question 15)

Thanks in advance.

Hi

As in any speed question, it’s useful to translate words into picture. Draw a line diagram.

In 1h John travelled 4km or 4000m faster than Mary. This means Mary is 2000m away from the midpoint.

2000m ------- 60min (1h)
100m ------- 3min
300m -------9min

They met at 9.09 am

John took 3 min and Mary took 9 min to travel the same distance.John was 3 times faster than Mary.

If John took 9 min, then Mary would take 27min
Total time taken by Mary ------36min

Mary would reach point B @ 9.36am

Best wishes

[benleetube]

tianzhu:

benleetube:

Hi all, everyone. Can you guys help me with this question? I am not sure if this question have been posted before, but here is it:


At 9 a.m., John was cycling from point A to point B. At the same time, Mary was cycling from point B to point A using the same route as John. Cycling at a speed of 4km/h faster than Mary, John would pass Mary 300m away from the midpoint.

(A) what time did they pass each other?

(B) if John took another 3 minutes to reach point B, what time would Mary reach point A?

(Appeared in catholic high SA2(prelim) paper as question 15)

Thanks in advance.

Hi

As in any speed question, it’s useful to translate words into picture. Draw a line diagram.

In 1h John travelled 4km or 4000m faster than Mary. This means Mary is 2000m away from the midpoint.

2000m ------- 60min (1h)
100m ------- 3min
300m -------9min

They met at 9.09 am

John took 3 min and Mary took 9 min to travel the same distance.John was 3 times faster than Mary.

If John took 9 min, then Mary would take 27min
Total time taken by Mary ------36min

Mary would reach point B @ 9.36am

Best wishes

Hi,

Thank you so much. It really helped me.

[Belle2011]

Dear all,

I need some help on this problem.

At a fitness carnival, 1600 people participated in a Mass Dance and Taiji. 30% of the 1300 Mass Dance participants were adults. 40% of the Taiji participants were children. During the break, some Mass Dance participants went on to participate in Taiji, while some Taiji participants went on to participate in the Mass Dance. After the change, 25% of the Mass Dance participants and 75% of the Taiji participants were adults. How many Mass Dance participants were there after the change?

model answer: 1260

Thank-you.

Cheers,
Belle.

[tianzhu]

Hi Belle


This question has been discussed in one of our earlier posts.

This question has two unknowns, and one can solve it with Simultaneously Equations(SE). If a student is comfortable with algebraic manipulation, he/she could use SE through substitution or elimination method. Otherwise, he/she may solve it with SE through visual representation using boxes or circles. In this question, I try to solve it using the letters of the alphabet to represent one unit of people in Mass dance and Taiji.

For Mass Dance
Number of adults ----- 390 (30% of 1300)
Number of children ----- 910

For Taiji
Number of adults ----- 180
Number of children ----- 120 (40% of 300)

After the break

D + DDD ------ where D shows the 25% of adults, DDD shows the remaining 75% making up the number of children in Mass Dance.

TTT + T ------ where TTT shows the 75% of adults, T shows the remaining 25% of children in Taiji

We have
D + TTT ------- 570
DDD + T ----- 1030

Solving the equations, we have D ------315

Therefore, the number of Mass Dance participants after the change is 315*4 which is 1260.

You may also take a look at a pictorial solution for a similar question.

There are 800 children in Group A. 30% of the children in Group A were boys. There were 400 children in Group B. 60% of the children in Group B were boys. After some transfer between the two groups, 25% of the children in Group A and 75% of the children in Group B were boys. What is the transfer from Group B to A?

Best wishes

http://farm6.static.flickr.com/5263/5738959768_cab69b70e7_z.jpg\">

[bobsg01]

Pri. 6 Vol. of Liquids question.


Thanks for helping. :scratchhead:

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[tianzhu]

benleetube:

Hi,
Thank you so much. It really helped me.

Hi

You're welcome.

Best wishes

[corneyAmber]

http://i53.tinypic.com/2qbsn04.jpg\">

[corneyAmber]

bobsg01:

Pri. 6 Vol. of Liquids question.


Thanks for helping. :scratchhead:

http://i54.tinypic.com/15ez0pg.jpg\">

Assuming p6 knows cube root?
Then it is easy, cube root of 216 = 6
Hence the l x b x h = 6 x 6 x 6 for container A.

If container B has the same height and breadth as container A, then to fill half of the tank = 15.4 x 6 x 3 = 277.2 cubic cm

Since container B has already 216 cubic cm of water, then 277.2-216 = 61.2 cubic cm has to be added to make it half-filled.