Tutor MathsGuru: Ask me for your burning Maths questions!

[corneyAmber]

Almighty:

Hi,


Please help to solve this problem.

Ken took 20 minutes to cycle from point X to Y. On his return journey he took only 12 minutes when he cycled 6 km/hr faster. What was the distance between point X and Point Y ?

Ans : 3 Km

Let d be the distance between X and Y.
Let s be the speed at first.

distance = speed x time

Travelling from X to Y,
20 mins = 1/3h
d = 1/3s
On return journey Y to X, d = (s+6)*1/5

XY=YX (distance)
1/3s = (s+6)*1/5
1/3s = 1/5s + 6/5
(5-3)/15s = 6/5
2/15 s = 6/5
s = 6/5 * 15/2 = 9km/h

Hence d = 1/3s = 1/3 * 9 = 3km

[Vanilla Cake]

Almighty:

Ken took 20 minutes to cycle from point X to Y. On his return journey he took only 12 minutes when he cycled 6 km/hr faster. What was the distance between point X and Point Y ?

Constant distance

20 min = 1/3 of an hour
12 min = 1/5 of an hour

Ratio of time
1/3 : 1/5
5 : 3

Ratio of speed
3 : 5

Difference = (5-3) units = 2 units
2 units = 6 km/h
1 unit = 3 km/h

Distance between point X and point Y = 3x3x1/3= 3 km.

[CoffeeCat]

Almighty:

CoffeeCat:

[quote=\"Almighty\"]Hi,


Can anyone help me to solve this problem?

What is the maximum number of right angled triangles, of base 5 cm and height 6 cm, that can be cut from a rectanglular sheet of paper, 49cm long and 34 cm wide?
Ans : 48

49/5 = 9 r 4. 49/6 = 8 r 1
34/5 = 6 r 4. 34/6 = 5 r 4

intuitively you want to minimise wastage so you should choose to cut the triangles with theheight 6 cm along the 49 cm long side, ie 8 times 6 = 48

Thankyou very much for the detailed quickest reply coffeecat[/quote]Actually Almight you might wana double check the given answer because as sun_2010 pointed out there are 2 mistakes in my working.

[YLH88]

Hi Mathsguru,


Need your help with the following questions :

1) The sum of 6 consecutive numbers is 72e.
What is the value of the smallest number ?
Give your answer in terms of e.

2) Every day, Samir reads 7 pages of a story book and Dion reads 2 pages more than Samir.
Dion starts to read only 5 days after Samir has started.
After some time, Dion has read 21 pages more than Samir.
How many pages has Samir read by then ?

3) Mr Tan sold golf balls in packs of five.
The original selling price of each pack of golf balls was $20.
He sold 60% of his golf balls at $20 per pack and the rest at a discount of 30%.
He collected $1,056 from the sale of all the golf balls.
How many golf balls did he sell altogther ?

4)The figure below shows two shaded rectangles A and B in a square WXYZ.
The area of rectangles A is 36 cm2 and the area of rectangle B is 24 cm2.
Find the area of the square.

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


Thank you so much!!

[Almighty]

Thankyou very much for the detailed quickest reply coffeecat[/quote]

Actually Almight you might wana double check the given answer because as sun_2010 pointed out there are 2 mistakes in my working.[/quote]

Oh!!! just saw Sun_2010 reply.But i dont understand the working…Can anyone explain in a more detailed manner? May be some other method??

Thankyou Vanilla cake for answering my speed querry…IT was very quick…Thankyou very much to Vanilla, Coffeecat and Sun_2010…

[Vanilla Cake]

YLH88:

1) The sum of 6 consecutive numbers is 72e.

What is the value of the smallest number ?
Give your answer in terms of e.

This question was first posted by http://www.kiasuparents.com/kiasu/forum/viewtopic.php?t=6373&postdays=0&postorder=asc&start=1300 on Wed May 19, 2010 8:37 am and was answered by http://www.kiasuparents.com/kiasu/forum/viewtopic.php?t=6373&postdays=0&postorder=asc&start=1300 on Wed May 19, 2010 9:44 am

YLH88:

3) Mr Tan sold golf balls in packs of five.
The original selling price of each pack of golf balls was $20.
He sold 60% of his golf balls at $20 per pack and the rest at a discount of 30%. He collected $1,056 from the sale of all the golf balls.
How many golf balls did he sell altogther ?

Original price of 1 pack of golf balls = $20
After 30% discount, selling price of 1 pack of golf balls = 70/100x$20=$14

60% of golf balls sold at $20
40% of golf balls sold at $14

60% = 3/5
40% = 2/5

Number of sets = 1056/(20x3)+(2x14) = 1056/( 60+28 )= 1056/88=12
Number of packs = 12x5 = 60
Number of golf balls = 60x5 = 300
Number of golf balls sold altogether by Mr Tan = 300.

[Vanilla Cake]

YLH88:

2) Every day, Samir reads 7 pages of a story book and Dion reads 2 pages more than Samir.Dion starts to read only 5 days after Samir has started. After some time, Dion has read 21 pages more than Samir.How many pages has Samir read by then ?

Number of pages read by Samir on a daily basis = 7
Number of pages read by Dion on a daily basis = 7+2 = 9
Difference = 9-7= 2 pages

After 5 days, Samir has read 7x5 = 35 pages (Dion is behind by 35 pages)
Number of pages for Dion to catch up = 21-(-35)=21+35=56

56 divided by the difference = 56/2 = 28 days
28x7=196
By then, Samir has read 196 pages.

YLH88:

4)The figure below shows two shaded rectangles A and B in a square WXYZ.The area of rectangles A is 36 cm2 and the area of rectangle B is 24 cm2.Find the area of the square.

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

Using guess and check,
Area of rectangle A = 36 cm² = 4cmx9cm
Area of rectangle B = 24 cm² = 3cmx8cm

Length of WX = 9cm+3cm = 12 cm
Length of WZ = 8cm+4cm = 12 cm

Area of the square = 12cmx12cm = 144 cm²

[Sun_2010]

Almighty:

Oh!!! just saw Sun_2010 reply.But i dont understand the working..Can anyone explain in a more detailed manner? May be some other method??

Hi Almighty.

I have done this pic, see if this helps out.
This is a little different from my first explanation.

The rectangle 34x49 can be cut into 2 rectangles - 24x49 and 10x49

[/img]

http://www.postimage.org/image.php?v=TsiMmw0

[Almighty]

Hi Almighty.


I have done this pic, see if this helps out.


Thankyou very much for taking so much effort just to explain me much clearer.

[YLH88]

Hi Vanilla Cake,


Thank you very much!