Q&A - PSLE Math

[MathIzzzFun]

jarenchuatw:

Help! How to solve this question?


A tank is 2/3 filled with water. It took 16minutes for a tap to drain this water completely. Another tap could fill the tank in 12 minutes when empty. If both the taps were turned on together, how long would it take for the tank to be completely filled with water?

Thanks in advance

Hi

Tank capacity --> 24 units
1st tap drain rate --> 2/3 x 24 units/16 min = 1 unit/min
2nd tap fill rate --> 24 units/ 12 min = 2 units/min
When both taps are turned on, nett fill rate --> 1 unit/min
2/3 tank filled, so 1/3 to fill --> 8 units to be filled
time taken to fill to full --> 8 units / 1 unit/min = 8 min

cheers.

[MathIzzzFun]

Spongy:

Hi, I need help in this question, thank you!

1. There are 4 cyclists, Alan, Bob, Cathy and Dan. Alan, Bob and Cathy started at the same point to overtake Dan, who was a distance ahead of them. Alan took 10h to overtake Dan and Bob took 2h to overtake Dan. The speed for Alan, Bob and Cathy are 4km/h, 5km/h and 10km/h as accordingly. What was the time taken by Cathy to overtake Dan?

Hi

there are a few approaches...here is one by working out the distances of the 4th cyclist Dan from start point...

When Bob overtake Dan (1st overtake), distance of Dan from start point = 2 x 5 = 10km
When Alan overtake Dan (2nd overtake), distance of Dan from start point = 10 x 4 = 40 km
Distance travelled by Dan from \"1st overtake\" to \"2nd overtake\" = 30 km, and time taken = 10h- 2h=8h
Dan's speed = 3.75km/h

Since Bob took 2h to overtake Dan, 2 x (5-3.75) = 2.5km --> Dan was 2.5 km from start point when Alan, Bob and Cathy started at start point.

10-3.75 = 6.25 km/h --> Cathy cycles 6.25 km/h faster than Dan
2.5/6.25 = 0.4h = 24 min --> cathy took 24 min to overtake Dan

cheers.

[CDE]

Hi, can anyone g ive the explanation & working on the following:


A rectangle divides a plane into 2 region at the most. How many regions at the most can 5 such identical rectangles divide the plane into?

No picture or anything else given. The answer is 82 regions, but how :?
TIA.

[jarenchuatw]

Thanks Master! Clear and concise explanation given.

[CDE]

MathIzzzFun:

jarenchuatw:

Help! How to solve this question?


A tank is 2/3 filled with water. It took 16minutes for a tap to drain this water completely. Another tap could fill the tank in 12 minutes when empty. If both the taps were turned on together, how long would it take for the tank to be completely filled with water?

Thanks in advance

Hi

Tank capacity --> 24 units
1st tap drain rate --> 2/3 x 24 units/16 min = 1 unit/min
2nd tap fill rate --> 24 units/ 12 min = 2 units/min
When both taps are turned on, nett fill rate --> 1 unit/min
2/3 tank filled, so 1/3 to fill --> 8 units to be filled
time taken to fill to full --> 8 units / 1 unit/min = 8 min

cheers.

MathIzzzFun, how do you get 24 units of tank capacity? It's not stated in question.

[tianzhu]

superhappy:

Michaelia0816:

Thx, Tianzhu, it is from PSLE Booklet, which my HW.

Hi, I need help on this question.

A rectangular tank was filled with water flowing from the tap.
At 10am, the tank was empty.
At 1pm, the tank was 1/3 filled with water.
At what time would the tank be 7/12 filled with water flowing from the tap.

Thank you

Hi

Good Morning.

I think this is a MCQ question.

A common multiple of 3 and 12 is 12.

1/3 filled ------ 4 units (1/3*12)

At 1pm ------- 4 units filled with water.

3h (180 minutes) ------- 4 units

45 minutes ------- 1 unit

135 minutes ------ 3 units (1/3 to 7/12)

From 1pm, add a duration of 135 minutes, I’ll leave it to students to work out the answer.

Best wishes

[tianzhu]

CDE:

Hi, can anyone g ive the explanation & working on the following:


A rectangle divides a plane into 2 region at the most. How many regions at the most can 5 such identical rectangles divide the plane into?

No picture or anything else given. The answer is 82 regions, but how :?
TIA.

Hi

Where is this question from?

I get an answer of 16(dividing the plane into regions).

Best wishes

[2DMommy]

Please help me with the two questions :


1) Mr Tan bought some thumbs drives for $340. If he was given 15% discount, he would be able to buy 4 more identical thumb dirves for the same amount of money. What was the original price of each thumb drives ?

2) Mr and Mrs Lim travelled in opposite directions after leaving their house at the same time. Mr Lim travelled towards Ponggol while Mrs Lim travelled towards Jalan Elias. Mrs Lim drove at a speed which was 12km/h slower than Mr Lim. After 25 min, Mr Lim had to turn back towards home for his misplaced keys while Mrs Lim continued with her journey to Jalan Elias without stopping. At 9am, the distance between Mr and Mrs Lim was 16 km. How far was Mrs Lim from her home at 9am?

Thank you !

[tianzhu]

2DMommy:

Please help me with the two questions :

1) Mr Tan bought some thumbs drives for $340. If he was given 15% discount, he would be able to buy 4 more identical thumb dirves for the same amount of money. What was the original price of each thumb drives ?

Hi

Amount saved by Mr Tan due to 15% discount ------- 15/100*340 ------- 51

With this amount, he’ll be able to buy 4 thumb drives @15%discount.

Discounted price of each thumb drive ------- 51/4 ------ 12.75

Original price per thumb drive ------ 12.75/0.85 ------- 15

Best wishes

[Michaelia0816]

Pls help with this too!

http://t.co/wf2cfrbz
And
1) A jar filled with 40 identical screws weighs 1.4 kg. The same jar when filled with 20 identical nails weighs 500 g. The mass of each screw is twice the mass of each nail. What is the mass of the empty jar?