Question

A chemical factory produces two kinds of unnatural amino acids: acid A and acid B. Of the acids produced by the factory last year, \( \frac{1}{3} \) were acid A and the rest were acid B. If it takes \( \frac{2}{5} \) as many hours to produce acid B per unit as it does to produce acid A per unit, then the number of hours it took to produce the acid B last year was what fraction of the total number of hours it took to produce all the acids?

• A. \( \frac{2}{5} \)
• B. \( \frac{4}{9} \)
• C. \( \frac{17}{35} \)
• D. \( \frac{1}{2} \)
• E. \( \frac{5}{9} \)

Hint:

When calculating fractions of a total, always use the total as the denominator and the relevant part as the numerator.

Answer 1

The Correct Option is B

Step 1: Understand the fractions.
Let the total number of acids produced be \( 1 \). The fraction of acid A produced is \( \frac{1}{3} \), and the fraction of acid B produced is \( 1 - \frac{1}{3} = \frac{2}{3} \). Let the time taken to produce one unit of acid A be \( t \). Then, the time taken to produce one unit of acid B is \( \frac{2}{5}t \).
Step 2: Set up the total time.
The total time taken to produce acid A is \( \frac{1}{3} \times t = \frac{t}{3} \), and the total time taken to produce acid B is \( \frac{2}{3} \times \frac{2}{5} t = \frac{4}{15} t \). The total time taken to produce both acids is: \[ \frac{t}{3} + \frac{4}{15} t = \frac{5}{15} t + \frac{4}{15} t = \frac{9}{15} t = \frac{3}{5} t \] Step 3: Find the fraction of total time for acid B.
The fraction of time spent on acid B is: \[ \frac{\frac{4}{15} t}{\frac{9}{15} t} = \frac{4}{9} \] Step 4: Conclusion.
The correct answer is (B) \( \frac{4}{9} \).