Bunuel wrote:

If 50 apprentices can finish a job in 4 hours and 30 skilled workers can finish the same job in 9/2 hours, how much of the job should be completed by 10 apprentices and 15 skilled workers in 1 hour?

(A) 1/9

(B) 29/180

(C) 26/143

(D) 1/5

(E) 39/121

Another way. Looks long. It isn't. Under 1:30

Find the rate of an individual apprentice and an individual skilled worker. Use that rate to figure out how much work gets finished when the number of workers change. (Just add # to the left side of the RT=W equation.)

Let # = number of workers

# * r * t = WIndividual rate of apprentice:

# = 50, r = ?? t = 4, W = 1

\(50 * r * 4 = 1\)

\(r_{a} = \frac{1}{(50*4)} = \frac{1}{200}\)

Individual rate of skilled worker:

# = 30, r = ??, t = 9/2, W = 1

\(30 * r *\frac{9}{2}= 1\)

\(r = \frac{1}{(30 * \frac{9}{2})}\)

\(r_{s} =\frac{1}{135}\)

Ten apprentices and 15 skilled workers, at their individual rates, work at respective collective rates.

10 apprentices' collective rate:

\((10 *\frac{1}{200}) =\frac{10}{200}=\frac{1}{20}\)15 skilled workers' collective rate:

\((15 *

\frac{1}{135}) =\frac{15}{135}=\frac{1}{9}\) Combined hourly rate of As and Ss:

\(\frac{1}{20} + \frac{1}{9} =\frac{29}{180}\)

Amount of work finished in one hour by all: \(\frac{29}{180} *

1 = \frac{29}{180}\)

Answer B