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 rateW = (# of workers) * (rate) * (time)
$250 = 5 * R * 6
R =
\(\frac{$250}{(5*6)}=\frac{$250}{30}=\frac{$25}{3}\)New scenario - use individual rateWith 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 1Work 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) =
$375Group 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) =
$300Total paint used (Total Work) =
($375 + $300) =
$675 worth of paint
Answer A
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