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08 Jan 2018, 23:46
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Difficulty:

45% (medium)

Question Stats:

59% (01:55) correct 41% (01:43) wrong based on 78 sessions

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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] ### Show Tags 09 Jan 2018, 01:28 3 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 $250 worth of paint working at the same rat [#permalink] ### Show Tags 06 Feb 2018, 09:07 each of the two new people are working twice as fast as the original people, so we can consider 2 of them as 4 of original people. Therefore, after 2 more people come, they will have total of 5 + 2*2 = 9 people. Apply the following: 5 people --- 6 hours --- 250$
9 people --- 9 hours --- x $(9/5) * (9/6) = (x/250). Solve for x we got x = 675 => Answers A SC Moderator Joined: 22 May 2016 Posts: 1765 In 6 hours, 5 painters use$250 worth of paint working at the same rat [#permalink]

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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 _________________ In the depths of winter, I finally learned that within me there lay an invincible summer. -- Albert Camus, "Return to Tipasa" Target Test Prep Representative Status: Head GMAT Instructor Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 2570 Re: In 6 hours, 5 painters use$250 worth of paint working at the same rat [#permalink]

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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.

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