Maths - Ratio Question or an algerberic equation?

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CTMertens
Posts: 1
Joined: Fri Jan 07, 2011 6:22 pm

Maths - Ratio Question or an algerberic equation?

Post by CTMertens »

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?
JGBallard
Posts: 88
Joined: Sun Jan 02, 2011 10:12 pm

Calling all mathematicians!

Post by JGBallard »

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. :D
workhard
Posts: 132
Joined: Sat Jul 31, 2010 4:31 pm

Re: Maths - Ratio Question or an algerberic equation?

Post by workhard »

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
hermanmunster
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Joined: Fri Sep 15, 2006 9:51 am
Location: The Seaside

Re: Calling all mathematicians!

Post by hermanmunster »

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. :D
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?
yoyo123
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Joined: Mon Jun 18, 2007 3:32 pm
Location: East Kent

Re: Maths - Ratio Question or an algerberic equation?

Post by yoyo123 »

simples
:wink:

2 birds with one stone!
JGBallard
Posts: 88
Joined: Sun Jan 02, 2011 10:12 pm

Re: Maths - Ratio Question or an algerberic equation?

Post by JGBallard »

Thank you thank you thank you!!!! :D Did spend some time trying to figure this out!
SunlampVexesEel
Posts: 1245
Joined: Fri Jul 06, 2007 9:31 pm

Re: Maths - Ratio Question or an algerberic equation?

Post by SunlampVexesEel »

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
yogkruti
Posts: 267
Joined: Sun Mar 21, 2010 6:06 pm

Re: Maths - Ratio Question or an algerberic equation?

Post by yogkruti »

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.
yoyo123
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Joined: Mon Jun 18, 2007 3:32 pm
Location: East Kent

Re: Maths - Ratio Question or an algerberic equation?

Post by yoyo123 »

thaks yogkruti,

one of those sneaky bits that they sneak into a question to check if you were really paying attention.
minubht80
Posts: 21
Joined: Sat Aug 21, 2010 5:53 pm

Re: Maths - Ratio Question or an algerberic equation?

Post by minubht80 »

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.

answer for 1

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)


Answer for 2

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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