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In 6 hours, 5 painters use $250 worth of paint working at the same rat

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In 6 hours, 5 painters use $250 worth of paint working at the same rat [#permalink]

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New post 08 Jan 2018, 23:46
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In 6 hours, 5 painters use $250 worth of paint working at the same rate per person. What is the cost of paint used in 9 hours if two more people each working twice as fast as each of the first 5 painters join the crew?

A. $675
B. $525
C. $450
D. $375
E. $325

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In 6 hours, 5 painters use $250 worth of paint working at the same rat [#permalink]

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New post 09 Jan 2018, 01:28
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Bunuel wrote:
In 6 hours, 5 painters use $250 worth of paint working at the same rate per person. What is the cost of paint used in 9 hours if two more people each working twice as fast as each of the first 5 painters join the crew?

A. $675
B. $525
C. $450
D. $375
E. $325



Since 5 painters working for 6 hours, use $250 worth of paint, 1 painter will use \($ (\frac{250}{5*6}) = $ (\frac{25}{3})\) worth of paint

We have been asked to find the cost of paint that will be used if 2 more painters working twice as fast as each of the 5 painters join the crew.

We will have \(5+2*2 = 9\) painters working for 9 hours, who will consume \(9*9*\frac{25}{3} = 27*25 = $675\) (Option A)
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Re: In 6 hours, 5 painters use $250 worth of paint working at the same rat [#permalink]

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New post 06 Feb 2018, 09:07
each of the two new people are working twice as fast as the original people, so we can consider 2 of them as 4 of original people. Therefore, after 2 more people come, they will have total of 5 + 2*2 = 9 people.

Apply the following:
5 people --- 6 hours --- 250$
9 people --- 9 hours --- x $

(9/5) * (9/6) = (x/250). Solve for x we got x = 675 => Answers A
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In 6 hours, 5 painters use $250 worth of paint working at the same rat [#permalink]

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New post 06 Feb 2018, 11:39
Bunuel wrote:
In 6 hours, 5 painters use $250 worth of paint working at the same rate per person. What is the cost of paint used in 9 hours if two more people each working twice as fast as each of the first 5 painters join the crew?

A. $675
B. $525
C. $450
D. $375
E. $325

This problem is similar to RT = W problems. "Work" is amount of paint used, measured in dollars.

You don't need the dollar sign in calculations. The answer must be in dollars. I included $ for clarity, but it can be counter-intuitive. The rate here means that 25 dollars' worth of paint is used every 3 hours.

Original scenario - Find individual rate
W = (# of workers) * (rate) * (time)
$250 = 5 * R * 6
R = \(\frac{$250}{(5*6)}=\frac{$250}{30}=\frac{$25}{3}\)

New scenario - use individual rate
With different rates for different workers:
1) calculate total "work" for the group of 5 (Group 1);
2) double the rate, calculate "work" for other 2 (Group 2);
3) add total work done by both groups

Paint used by Group 1
Work done by group of 5 painters at rate = \(\frac{$25}{3}\) for 9 hours
W\(_{group1}\) = (# of workers) * R * T
W\(_{group1}\) = 5 * (\(\frac{$25}{3}\)) * 9 = ($125*3) = $375

Group 2 painters work twice as fast as Group 1 painters.
Group 1 individual rate = \(\frac{$25}{3}\)
Group 2 individual rate:\(\frac{$25}{3}*2 = \frac{$50}{3}\)

Paint used by Group 2:
W\(_{group2}\) = (# of workers) * R * T
W\(_{group2}\) = (2) *(\(\frac{$50}{3}\)) * (9) = ($100*3) = $300

Total paint used (Total Work) =
($375 + $300) = $675 worth of paint

Answer A
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Re: In 6 hours, 5 painters use $250 worth of paint working at the same rat [#permalink]

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New post 12 Feb 2018, 17:09
1
Bunuel wrote:
In 6 hours, 5 painters use $250 worth of paint working at the same rate per person. What is the cost of paint used in 9 hours if two more people each working twice as fast as each of the first 5 painters join the crew?

A. $675
B. $525
C. $450
D. $375
E. $325


The rate of each of the first 5 painters is (250/5)/6 = 50/6 = 25/3 dollars per hour. Thus the rate of each of the two new painters is 50/3 dollars per hour.

For 9 hours, the first 5 painters will use 5 x 25/3 x 9 = 375 dollars of paint and the 2 new painters will use 2 x 50/3 x 9 = 300 dollars of paint. Thus a total of 375 + 300 = 675 dollars of paint will be used.

Answer: A
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Re: In 6 hours, 5 painters use $250 worth of paint working at the same rat   [#permalink] 12 Feb 2018, 17:09
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In 6 hours, 5 painters use $250 worth of paint working at the same rat

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