Q&A - PSLE Math

[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

[Winx5015]

Hi, I need help for this question.


The distance between Town A and Town B is 116km. A bus left Town A and headed for Town B. Some time later, a car left Town A and headed for Town B along the same route. Along the way, the car overtook the bus and arrived at Town B 45 minutes earlier than the bus. when the car arrived at Town B, the bus had travelled 5/8 of the distance. What was the speed of the bus?

Thanks:)

[Mychildren]

Would like to try Winx5015 question:


The bus still have 3/8 of the total distance to travel, that is 3/8 of 116km = 43.5km
The car arrived 45min earlier whereby the bus still need to travel 43.5km to reach Town B.

Therefore, the bus need to travel 43.5km in 45min.
So speed of bus is ----> 43.5km in 3/4 hour (45min out of 60min)

Model diagram comes in here.
3 part of 4 is 43.5km
4 part of 4 is 56km

Ans: 56km/h

(tianzhu, correct me if I’m wrong. My brain hungry for math questions so come here kapo.)

[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