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 Post subject: Maths - Ratio Question or an algerberic equation?Posted: Fri Jan 07, 2011 5:35 pm

Joined: Fri Jan 07, 2011 5:22 pm
Posts: 1
Can anyone help -it's a question on ratios or an algerberic equation:

It takes 2 decorators 8 days to paint a house.
One is lazy and one is energetic.

Energetic can paint the house in 12 days on his own.
How many days would it take lazy to paint the house on his own?

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 Post subject: Calling all mathematicians!Posted: Fri Jan 07, 2011 5:43 pm

Joined: Sun Jan 02, 2011 9:12 pm
Posts: 88
Can someone please help with these questions , I cannot work them out - any help much appreciated:

1. It takes 2 decorators 8 days to paint a house. On is lazy, the other is energetic. The energetic one could paint the house in 12 days on his own. How many days would it take the lazy one to paint the house on his own?

2.A number of children are standing in a circle. They are evenly spaced and the 7th child is directly opposite the 18th child. How many children are there altogether?

Thank you ...these are from a St Pauls sample paper.

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 Posted: Fri Jan 07, 2011 5:55 pm

Joined: Sat Jul 31, 2010 3:31 pm
Posts: 132
Hi!

E takes 12 days for 1 house by himself. So in 8 days he paints 8/12 (or 2/3) of a house:

12 days .......... 1 house

divide both sides by 12

1 day...............1/12 of house

multiply both sides by 8

8 days.............8/12 of house (same as 2/3 house, divide top and bottom by 4)

So, working with L, E painted 2/3 of the house. So L painted only the remaining 1/3 of it. (We are told that the house was finished in 8 days.)

So L to E is 1/3 to 2/3, or 1 to 2. L is half as productive as E, which means L will take twice as long.

So L will take 12 x 2 (or 24) days to paint the whole house by himself.

Hope this helps.

WH

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 Post subject: Re: Calling all mathematicians!Posted: Fri Jan 07, 2011 5:56 pm

Joined: Fri Sep 15, 2006 8:51 am
Posts: 8113
JGBallard wrote:
Can someone please help with these questions , I cannot work them out - any help much appreciated:

1. It takes 2 decorators 8 days to paint a house. On is lazy, the other is energetic. The energetic one could paint the house in 12 days on his own. How many days would it take the lazy one to paint the house on his own?

2.A number of children are standing in a circle. They are evenly spaced and the 7th child is directly opposite the 18th child. How many children are there altogether?

Thank you ...these are from a St Pauls sample paper.

1. decorator 1 does 1/12 of a house each day - so in 8 days he will do 2/3 of the house, so deco 2 does 1/3 in 8 days hence will take 24 days to do the whole lot

2 Not so sure abou this one but between 7 and 18 there are 10 numbers so there will be ten kids each side of the semicircle + child 7 and child 18 = total of 22?

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 Posted: Fri Jan 07, 2011 6:02 pm

Joined: Mon Jun 18, 2007 2:32 pm
Posts: 6966
Location: East Kent
simples

2 birds with one stone!

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 Posted: Fri Jan 07, 2011 6:07 pm

Joined: Sun Jan 02, 2011 9:12 pm
Posts: 88
Thank you thank you thank you!!!! Did spend some time trying to figure this out!

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 Posted: Fri Jan 07, 2011 6:37 pm

Joined: Fri Jul 06, 2007 8:31 pm
Posts: 1192
It's been a long week so these are guesses!

Fast has only 8 days so does 8/12 of a house before getting paid... 4/12 = 1/3 left

1/3 takes lazy eight days... so a whole house would take lazy 8x3=24 days

i.e. fast works twice as fast as lazy

For the circle....

If 7 is opposite 18, 6 would be opposite 17, 5 opposite 16, 4 opposite 15, 3 opposite 14, 2 opposite 13, 1 opposite 12. So half the circle is 12 so a full circle is 24.

Regards
SVE

_________________
Animis opibusque parati

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 Posted: Fri Jan 07, 2011 6:50 pm

Joined: Sun Mar 21, 2010 5:06 pm
Posts: 267
Half circle is 12, but the full circle will be 22 since we have already counted the 2 on the boundaries.

So should be 22.

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 Posted: Sat Jan 08, 2011 9:34 am

Joined: Mon Jun 18, 2007 2:32 pm
Posts: 6966
Location: East Kent
thaks yogkruti,

one of those sneaky bits that they sneak into a question to check if you were really paying attention.

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 Posted: Thu Jan 20, 2011 11:02 pm

Joined: Sat Aug 21, 2010 4:53 pm
Posts: 21
Theory has already been discussed above, as this is going to be 11plus exam where time is constraint, below is the shortcut way of doing it. As a parent I would first explain my child with theory and how to do it and lateron, share the shortcut method to save time.

a*b/(b-a) = 12*8/(12-8)
96/4 = 24

b - number of days one person complete the task
a - number for days both working togther shall complete the task

Above is the simpler version of calculation, it saves time in order to take one variable to other side of the equation and also find the lcm of both of numbers..

One more example little bit different, if one worker takes 4 days and another take 8 takes, in how much time both shall complete the work
In such case

a*b/(a+b)

7th and 18th are the diameter end of same circle so difference X 2 should be the total number of child.

Regards
jmom

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