This blog is managed by Song Hock Chye, author of Improve Your Thinking Skills in Maths (P1-P3 series), which is published and distributed by EPH.

Tuesday, February 17, 2009

Nanyang Pri Sch P6 CA1 2008 Math Q38

Two identical taps, when turned on at the same time, take 5 minutes to release 10 litres of water. How many such taps, when turned on at the same time, are needed to release 27 litres of water in 3 minutes?

Solution

2 taps, 5 min ----- 10 litres
2 taps, 1 min ----- 10 litres divided by 5 = 2 litres
1 tap, 1 min ----- 2 litres divided by 2 = 1 litre

27 litres, 1 min ----- 27 litres x 1 = 27 litres

27 litres, 3 min (3x slower than 1 min)
----- 27 divided by 3 = 9

Answer: It took 9 taps

22 comments:

Anonymous said...

Hi all,

I have a question with regards to the topic which is Speed.

In speed, is it true that the distance is proportional to the speed and time.

What is the meaning of Proportion in Speed?

Anonymous said...

I hear speed can be solve using this unit method? Anyone hear before?

Show me said...

Hi anon @0112

Please show an example.
Best Wishes

xiaorou said...

Hi anon @0112

We are curious about how UTM can help to solve speed problems.

Speed is one of the more challenging PSLE Maths topics.It baffles students and many parents.

Would you like to show how it works on this question?

1)Sarah took 15 minutes to jog from her home to a swimming pool. After swimming, she took 20 minutes to walk the same way home. Her walking speed was 3 km/h slower than his jogging speed. Find Sarah's walking speed in km/h.

Anonymous said...

This can be done without using UTM.

Express the time in hours.

15/60 = 1/4 hr

we can look at this question in a different point of view.

Jogging speed is faster than walking speed by 3 km/h

Jogging = 1/4 hr * 3 km/h
= 3/4 km more.

The time taken to cover the remaining distance by walking is 5 mins (20 - 15) or 1/12 hr

1/12 hr -----> 3/4 km
1 hr -----> 9 km/h

Thus, the walking speed is 9 km/h.

xiaorou said...

Hi
anon@0923

Are you the same person as anon @0112?

Why don't you give yourself a nick?Less confusing this way.

xiaorou said...

Hi anon anon@0923

Not sure if you are the same person as the earlier anon.

We are just curious to see if UTM can help in solving speed problems.

Anonymous said...

i think this question is from the paper i got full maRKS

Anonymous said...

i think this question is from the paper i got full maRKS

Anonymous said...

I hear there is a blog that demonstrate UTM to oslve speed...any one got any idea?

Anonymous said...

I strongly believe that Speed can be easily solved by drawing distance line. Most schools have taught students how to solve speed problems.

However, UTM is a much complicated model compare to model drawing.

Unlike UTM, model drawing allows students to visualise what is happening and can be easily comprehended.

Anonymous said...

what is UTM?

tough said...

I have a P6 Maths question and hope that someone out there can provide me with the solution.

Question:

Johnny left from his house for his school. He walked 3 steps forward and then moved 1 step back. Each step he took is 1 m. It took him 3 minutes to walk 1 m and 1 minute to move back . Assuming that his speed for walking every step is constant,

find (a) the distance he had walked after 30 minutes.

(b) the time he took to reach his school if the distance from his house to his school is 60 m.

xiaorou said...

Hi
Hope this is of some use

a)In 8 mins, he walked 2m
In 30 mins, he walked (2*30)/8, which is 7.5m

b)He took 8 mins to cover 2m
Therefore , he took (60*8)/2, which is 240 mins or 2 hrs

Just wondering, why he took 3 mins to move 1 step forward and 1 min to move 1 step backwards

xiaorou said...

Hi
Hope this is of some use

a)In 8 mins, he walked 2m
In 30 mins, he walked (2*30)/8, which is 7.5m

b)He took 8 mins to cover 2m
Therefore , he took (60*8)/2, which is 240 mins or 2 hrs

Just wondering, why he took 3 mins to move 1 step forward and 1 min to move 1 step backwards

tough said...

This is the correct question.

Question:

Johnny left from his house for his school. He walked 3 steps forward and then moved 1 step back. Each step he took is 1 m. It took him 3 seconds to walk 3 m and 1 second to move back . Assuming that his speed for walking every step is constant,

find (a) the distance he had walked after 30 minutes.

(b) the time he took to reach his school if the distance from his house to his school is 60 m.

xiaorou said...

Hi tough
Hope this is of some use.

a)In 8secs, he walked 2m
In 30mins, he walked (2*1800)/8, which is 450m

b)He took 8secs to cover 2m
Therefore , he took (60*8)/2, which is 240sec or 4mins

xiaorou said...

Hi
Sorry,I made some mistakes earlier.The revised answer is
a)In 2secs, he walked 2m
In 30mins, he walked (2*1800)/2, which is 1800m

b)He took 2secs to cover 2m
Therefore , he took (60*2)/2, which is 60sec or 1min

Anonymous said...

use listing and look for pattern. Similar to a 2008 PSLE question

xiaorou said...

Hi
Sorry, I made some mistakes earlier.

The revised answer is
a)In 4secs, he walked 2m
In 30mins, he walked (2*1800)/4, which is 900m

b)He took 4secs to cover 2m
Therefore , for the first 58m, he took (58*4)/2, which is 116secs
He took another 2 secs to cover the remaining 2m.
Therefore, he took 118secs.

Please consider my earlier replies as null and void.

Anonymous said...

Excuse me...but i dont understand

xiaorou said...

Hi anon 0353

suggest you see your teacher,nothing can replace a teacher explaining to you face to face.

Best wishes