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PostPosted: Thu Sep 20, 2012 8:49 am 
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Pl help with this question-

It takes 2 decorators 8 days to paint a house.
One is lazy and one is energetic.
Energetic can paint the whole house in 12 days on his own.
How many days would it take lazy to paint the house on his own?

Thanks ...


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PostPosted: Thu Sep 20, 2012 9:03 am 
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Joined: Thu Jun 14, 2012 9:28 am
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pndt.snl wrote:
Pl help with this question-

It takes 2 decorators 8 days to paint a house.
One is lazy and one is energetic.
Energetic can paint the whole house in 12 days on his own.
How many days would it take lazy to paint the house on his own?

Thanks ...


If the energetic one paints the whole house in 12 days, then he paints 8/12= 2/3 of the house in 8 days. Thus, the lazy paints 1/3 of the house in 8 days (since both of them working together complete the job in 8 days). It follows then it would take the lazy one 24 days to paint the whole house on his own.
T


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PostPosted: Thu Sep 20, 2012 9:08 am 
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Joined: Tue Jul 21, 2009 9:56 pm
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I'm sure there are lots of ways to think about it, but this is my method. Let's say the area of the house is A.

Energetic must paint A/12 per day because he can complete the job in 12 days on his own.

Say Lazy's amount per day is L.

We know that 8 x Lazy's amount per day + 8 x energetic's amount per day = A

This is because we are told that together they can paint the whole house in 8 days

So 8 L + 8 x A/12 = A

If you re-organise this you get that L = A/24

This tells you that Lazy can paint 1/24th of the house on his own each day. So it would take him 24 days on his own to paint the whole house.


Last edited by mystery on Thu Sep 20, 2012 10:10 am, edited 1 time in total.

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PostPosted: Thu Sep 20, 2012 9:10 am 
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Our posts crossed! Your way is neater. In the heat of an exam I'd do it my way because my formal algebra sticks but my reasoning goes! Every child is different.


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PostPosted: Thu Sep 20, 2012 10:03 am 
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Thank you so much.
Really appreciate it !!


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PostPosted: Thu Sep 20, 2012 10:11 am 
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Sorry there was a typo in my workings which I have just edited. I hope I didn't cause any confusion.


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