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

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

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

rt=d
5r6=250
r=250/30=25/3
2 more twice as fast = 4r
9r9=9(25/3)*9=27*25=675

Ans (A)