Tutor MathsGuru: Ask me for your burning Maths questions!

[Herbie]

Hi Dharma


I have one qn, please see below

Mr Tan took 6 hours to drve from Town A to Town B.
Mr Lm who started at the same time as Mr Tan took 4 hours to drive from Town B to Town A

When they met each other, they were 48km away from mid point of Town A and Town B

(a) Calculate the distance between Town A and Town B
(b) Calculate the speed of Mr Tan


Working
Time
Tan : Lim
6: 4


Ratio of Speed/Distance
Tan: Lim
6: 4
2:3

3u- 2u = 1u
Iu = 48km
10u = 48km x 10
=480km

(b)480/6 = 80km/h

Is the working for (a) correct??


Thanks and regards,

[Almighty]

Almighty:

Hi all,

The question :
A rectangular block of wood, 47 cm long, 38 cm wide, and 24 cm high , was cut into equal cubes of edge 4 cm.
a) What was the maximum number of 4cm cubes which I could cut?
b) What was the total surface area of the remaining piece of wood?

a) my answer : 594 cubes
b) Book answer : 256cm2. My answer is different.Can anyone halp on
section(B)
Thankyou in advance..

Hi Dharma Sir,
This question of mine is unanswered/Can u help me with sec (B)?
Thankyou

[Dharma]

Herbie:

Hi Dharma


I have one qn, please see below

Mr Tan took 6 hours to drve from Town A to Town B.
Mr Lm who started at the same time as Mr Tan took 4 hours to drive from Town B to Town A

When they met each other, they were 48km away from mid point of Town A and Town B

(a) Calculate the distance between Town A and Town B
(b) Calculate the speed of Mr Tan


Working
Time
Tan : Lim
6: 4


Ratio of Speed/Distance
Tan: Lim
6: 4
2:3

3u- 2u = 1u
Iu = 48km X 2 = 96km
5u= 96km x 5=480km

(b)480/6 = 80km/h

Is the working for (a) correct??


Thanks and regards,

Hi Herbie,

For part (a) I would have done as below. You answer is correct but I'm not able to follow the working.

When distance is constant (Town A to Town B)
Time ratio => Tan : Lim = 3 : 2
Speed ratio => Tan : Lim = 2 : 3

When they meet each other, they would have travelled the same time (time is constant). Tan would have travelled 2u and Lim travelled 3u when they met. Total distance between the 2 towns is 5u. So, Lim had travelled (5u/2 + 48km) before he met Tan.

For your working, I amended in red to make it clear.

a)\t3u – (5u/2) = 48km
1u = 48km x 2 = 96km
Distance between Town A and B = 5u = 5 x 96km = 480km

b) Speed of Mr Tan = 480km/6hrs = 80km/hr

[Dharma]

Almighty:

Almighty:

Hi all,

The question :
A rectangular block of wood, 47 cm long, 38 cm wide, and 24 cm high , was cut into equal cubes of edge 4 cm.
a) What was the maximum number of 4cm cubes which I could cut?
b) What was the total surface area of the remaining piece of wood?

a) my answer : 594 cubes
b) Book answer : 256cm2. My answer is different.Can anyone halp on
section(B)
Thankyou in advance..

Hi Dharma Sir,
This question of mine is unanswered/Can u help me with sec (B)?
Thankyou

Hi Almighty,

Pls refer to Tianzhu's very clear illustration. Thanks

[tianzhu]

Dharma:

b) Area = 2[ (24 x 3) + (24 x 2) + (3 x 2) ]cm2 = 252cm2

Hi Dharma

If you consider cutting out a big block of 44*36*24 to get 594 smaller cubes of 4cm, you’ll end up with an L shaped remainder.

Depending on how the cuts are done, you can have an L shaped remainder or a remainders of two rectangular blocks.

Best wishes

[Dharma]

tianzhu:

Dharma:

b) Area = 2[ (24 x 3) + (24 x 2) + (3 x 2) ]cm2 = 252cm2

Hi Dharma

If you consider cutting out a big block of 44*36*24 to get 594 smaller cubes of 4cm, you’ll end up with an L shaped remainder.

Depending on how the cuts are done, you can have an L shaped remainder or a remainders of two rectangular blocks.

Best wishes

Don't understand Tianzhu. If block of 44cm x 36cm x 24cm is cut into 4cm
cubes, there will not be anything remainder çause we get 594 nos of 4cm cubes.

Kindly explain. Thanks

[tianzhu]

Dharma:

Don't understand Tianzhu. If block of 44cm x 36cm x 24cm is cut into 4cm

cubes, there will not be anything remainder çause we get 594 nos of 4cm cubes.

Hi Dharma

I mean the remainder from the original block (47 cm long, 38 cm wide, and 24 cm high) after cutting away 44*36*24.

Best wishes

[Dharma]

tianzhu:

Dharma:

Don't understand Tianzhu. If block of 44cm x 36cm x 24cm is cut into 4cm

cubes, there will not be anything remainder çause we get 594 nos of 4cm cubes.

Hi Dharma

I mean the remainder from the original block (47 cm long, 38 cm wide, and 24 cm high) after cutting away 44*36*24.

Best wishes

Thanks Tianzhu. I see it now

[tiger262]

Dharma:

Almighty:

[quote=\"Almighty\"]Hi all,

The question :
A rectangular block of wood, 47 cm long, 38 cm wide, and 24 cm high , was cut into equal cubes of edge 4 cm.
a) What was the maximum number of 4cm cubes which I could cut?
b) What was the total surface area of the remaining piece of wood?

a) my answer : 594 cubes
b) Book answer : 256cm2. My answer is different.Can anyone halp on
section(B)
Thankyou in advance..

Hi Dharma Sir,
This question of mine is unanswered/Can u help me with sec (B)?
Thankyou

b) Area = 2[ (24 x 3) + (24 x 2) + (3 x 2) ]cm2 = 252cm2
(This is based on a remainder block of 24cm x 3cm x 2cm) - if u cut of 44cm from 47cm beginning from the one end.

But if if cut off 44cm from the centre portion of the 47cm length you may get different areas of the remaining shape depending how you make the next along the width.[/quote]Hi Dharma,

If we cut 44 cm from 47 cm beginning from one end, we will be left with an L-shaped block consisting of:

(a) Lengthwise, the 3 cm left out from 47 cm (after using up 44 cm)
(b) Breadthwise, the 2 cm left out from 38 cm (after using up 36 cm)
(c) Heightwise, the full 24 cm tall

Am I correct in my analysis? If I am correct, I cannot understand how its surface area can be as small as 252 sq cm.

Kindly explain your answer in more detail and point out where I am wrong.


Hi Tianzhu,

You have a great mastery in producing marvellous pictures and drawings. I will be most grateful if you can post the drawing of the L-shaped block that I have referred above. Your drawing will illustrate the dimensions of the remainder-block much more lucidly for all to understand. Please try if you can spare time.


Thanks to both you and Dharma.

[Dharma]

tiger262:

Dharma:

[quote=\"Almighty\"]
Hi Dharma Sir,
This question of mine is unanswered/Can u help me with sec (B)?
Thankyou

b) Area = 2[ (24 x 3) + (24 x 2) + (3 x 2) ]cm2 = 252cm2
(This is based on a remainder block of 24cm x 3cm x 2cm) - if u cut of 44cm from 47cm beginning from the one end.

But if if cut off 44cm from the centre portion of the 47cm length you may get different areas of the remaining shape depending how you make the next along the width.

Hi Dharma,

If we cut 44 cm from 47 cm beginning from one end, we will be left with an L-shaped block consisting of:

(a) Lengthwise, the 3 cm left out from 47 cm (after using up 44 cm)
(b) Breadthwise, the 2 cm left out from 38 cm (after using up 36 cm)
(c) Heightwise, the full 24 cm tall

Am I correct in my analysis? If I am correct, I cannot understand how its surface area can be as small as 252 sq cm.

Kindly explain your answer in more detail and point out where I am wrong.

Thanks to both you and Dharma.[/quote]Hi tiger262,

You are right. The area should be the area of the L-shaped block.