Tutor MathsGuru: Ask me for your burning Maths questions!

[CoffeeCat]

Lol yea what a mistake I had made. I have edited it. Thx for pointing out!

[Vanilla Cake]

Dharma:

liketoeat:

Hi, please help me solve this question. Thank you.


Candle A and candle B were placed on a table. Candle A was 1.5 cm longer than candle B. Candle A and candle B were lighted at 0630 h and 0800 h respectively. They burnt down to the same length at 1030 h. At 1200 h, candle B was burnt out while A only burnt out at 1230 h. Given that the rate of burning of each candle was constant throughout, find the original length of each candle. (Ans: candle A 13.5 cm; candle B 12 cm)

Time ratio => A : B = 4 : 3
Burning rate ratio => A : B = 3 : 4

Time taken to burn completely
A : 6 hrs (0630hrs to 1230hrs)
B : 4 hrs (0800hrs to 1200hrs)

Length (A ) = 3u x 6 = 18u
Length (B) = 4u x 4 = 16u

18u – 16u = 2u = 1.5cm
Original Length (A) = 18u = 9 x 1.5cm = 13.5cm
Original Length (B) = 16u = 8 x 1.5cm = 12.0cm

Hi liketoeat,
Could you pls advise the source of this question as this question requires some thinking? Is this question from school's homework?

Just to share 2 different alternatives for readers.One not using inverse ratio and one using model drawings (posted by the forever helpful Uncle Observer).Another method is algebra which I will not post here.

Alternative method 1
Same height to burn out completely ie equal burnt length
Candle A from 1000 h to 1230 h took 2 hours
Candle B from 1030 h to 1200 h took 1.5 hours

Find lowest common multiple of 1.5 and 2
Multiples of 2 = 2,4,6,8,10.......
Multiples of 1.5 = 1.5,3,4.5, 6, 7.5.......

So, LCM of 1.5 and 2 is 6.

Burning rates
Candle A = 6u/2 = 3u/hour
Candle B = 6u/1.5 = 4u/hour

From start to burn out completely
Candle A: 0630 h to 1230 h ie 6 h -> 6x3u=18u
Candle B: 0800 h to 1200 h ie 4 h -> 4x4u=16u

Candle A was 1.5 cm longer than candle B (Given),
18u-16u=1.5
2u=1.5
u = 0.75

Original length of candle A = 18u = 18x0.75 = 13.5 cm
Original length of candle B = 16u = 16x0.75 = 12 cm

Alternative method 2
By http://psle2010a.blogspot.com/2010/07/challenging-p6.html as posted by the kind and helpful Uncle Observer.

[mathsguru]

Dear all...


Just to let you all know tt I'm back... :peekaboo:

:imsorry: My sincere apologies for not being active for the past month. I've taken a 2-week break during the June hols and when I came back, I was busy conducting lessons. :faint:

Finally can catch a breather now since school re-opened! Many thanks to all kind souls who have been helping out here...so many pages to catch up for me!

Hmm...guess I will start solving questions posted from now on instead of trying to catch up with the backlog. Hehe...Hope to seek your understanding!! :please:

Cheers,
MathsGuru

[ruyu]

mathsguru:

Dear all...


Just to let you all know tt I'm back... :peekaboo:

:imsorry: My sincere apologies for not being active for the past month. I've taken a 2-week break during the June hols and when I came back, I was busy conducting lessons. :faint:

Finally can catch a breather now since school re-opened! Many thanks to all kind souls who have been helping out here...so many pages to catch up for me!

Hmm...guess I will start solving questions posted from now on instead of trying to catch up with the backlog. Hehe...Hope to seek your understanding!! :please:

Cheers,
MathsGuru

Yeah Mathsguru is back!

[mathsguru]

Ngserene617:

Hi kindly assist me for the below 3 stated questions, thanks.


1. Alex, Bryan and Charles paid for a meal. Alex paid 1/5 of the amount Bryan and Charles paid together. Bryan paid 1/4 of the amount Alex and Charles paid. If the meal cost $205.20, how much did Alex pay ?

2. Terry had $420 more than Sean. Sean gave Terry $72. Now, Sean has 1/7 as much money as Terry. How much money had Terry at first?

3. 3 sisters, Amy, Bonnie and Cindy shared to buy a present for their mother. Amy paid 1/3 of the amount which Bonnie and Cindy paid. Bonnie paid 1/5 of the amount which Amy and Cindy paid. If Cindy paid $30 more than Bonnie, how much did the present cost?

Thanks kindly help me to solve this !

Hi Ngserene617,

Since you have pm-ed me regarding these questions, I'm posting my solutions here for your reference (though they have been solved by other maths experts here).

Hope they can add to your child's understanding!

Cheers,
MathsGuru

http://www.postimage.org/image.php?v=aVzUgIi

http://www.postimage.org/image.php?v=aVzUjcr

http://www.postimage.org/image.php?v=aVzUobJ

[livewith_vanilla]

Here is a question I would like some help in.


Source: School paper
Level: P6

A train traveled through a 6500-metre tunnel at an average speed of 25m/s. The whole train took 4 min 30 s to pass through the tunnel completely.
What is the length of the train?

TIA.

[MOE Hater]

livewith_vanilla:

Here is a question I would like some help in.


Source: School paper
Level: P6

A train traveled through a 6500-metre tunnel at an average speed of 25m/s. The whole train took 4 min 30 s to pass through the tunnel completely.
What is the length of the train?

TIA.

25m/s x 4 min 30 s = 25m/s x 270s = 6750m
6750m - 6500m = 250m

The train is 250m long.

[mathsguru]

livewith_vanilla:

Here is a question I would like some help in.


Source: School paper
Level: P6

A train traveled through a 6500-metre tunnel at an average speed of 25m/s. The whole train took 4 min 30 s to pass through the tunnel completely.
What is the length of the train?

TIA.

Hi livewith_vanilla,

Here's my solution. Hope it helps!


MathsGuru

http://www.postimage.org/image.php?v=gxuHLp0

[livewith_vanilla]

mathsguru:

livewith_vanilla:

Here is a question I would like some help in.


Source: School paper
Level: P6

A train traveled through a 6500-metre tunnel at an average speed of 25m/s. The whole train took 4 min 30 s to pass through the tunnel completely.
What is the length of the train?

TIA.

Hi livewith_vanilla,

Here's my solution. Hope it helps!


MathsGuru

http://www.postimage.org/image.php?v=gxuHLp0

Thanks very much!

Edit: My solution was the same, though I didn't get it. Now i understand.:D

[Almighty]

liketoeat:

Dharma:

[quote=\"liketoeat\"]Hi, please help me solve this question. Thank you.


Candle A and candle B were placed on a table. Candle A was 1.5 cm longer than candle B. Candle A and candle B were lighted at 0630 h and 0800 h respectively. They burnt down to the same length at 1030 h. At 1200 h, candle B was burnt out while A only burnt out at 1230 h. Given that the rate of burning of each candle was constant throughout, find the original length of each candle. (Ans: candle A 13.5 cm; candle B 12 cm)

Time ratio => A : B = 4 : 3
Burning rate ratio => A : B = 3 : 4

Time taken to burn completely
A : 6 hrs (0630hrs to 1230hrs)
B : 4 hrs (0800hrs to 1200hrs)

Length (A ) = 3u x 6 = 18u
Length (B) = 4u x 4 = 16u

18u – 16u = 2u = 1.5cm
Original Length (A) = 18u = 9 x 1.5cm = 13.5cm
Original Length (B) = 16u = 8 x 1.5cm = 12.0cm

Thank you, Dharma.[/quote]Hi Dharma,
Can u pls. explain how u get this step? :?
Time ratio => A : B = 4 : 3