Working together at their respective constant rates, Machine

The prompt should read as follows:

BTGmoderatorDC wrote:Working together at their respective constant rates, Machine A and Machine B can produce 1,200 units in 8 hours. Working alone, Machine B would complete that same output in 50% more time. If Machine A were to work on its own for an 8-hour shift, APPROXIMATELY what percent of the 1,200 unit total would it produce?

A. 25
B. 33
C. 50
D. 67
E. 75

Since A+B take 8 hours to produce 1200 units, the combined rate for A+B = w/t = 1200/8 = 150 units per hour.

Since B take 50% more time than the 8 hours required when A+B work together, B's time = 8 + (50% of 8) = 8 + 4 = 12 hours.
Since B takes 12 hours to produce 1200 units, B's rate alone = w/t = 1200/12 = 100 units per hour.
Thus, A's rate alone = (combined rate for A+B) - (B's rate alone) = 150 - 100 = 50 units per hour.

The two rates in blue indicate the following:
Of the 150 units produced by A+B each hour, 50 units are produced by A, implying that (A's work)/(total work) = 50/150 = 1/3 ≈ 33.33%.

The correct answer is B.

- Machine A and Machine B can produce 1,200 units in 8 hours \(\Rightarrow\) in 1 hour they can produce \(\frac{1200}{8} = 150\) units.

- Machine B would complete that same output in 50% more time \(\Rightarrow\) to produce 150 units, it takes B: 1,5 hours. \(\Rightarrow\) In 1 hour B can produce: \(150: 1,5 = 100\) units.

\(\Rightarrow\) In 1 hour A can produce: \(150 - 100 = 50\) units.
\(\Rightarrow\) If Machine A were to work on its own for an 8-hour shift, it can produce: \(50\cdot 8 = 400\) units \(= 33.33\)% of total 1200 units.

Hence the answer is __B__.