A manufacturing assembly line produces a batch of B electronic components in h hours. To i… — ACT

A manufacturing assembly line produces a batch of $B$ electronic components in $h$ hours. To increase efficiency, a new assembly line is installed that can produce the same batch of components in $\frac{1}{3}$ of the time. Which of the following expressions represents the rate, in components per hour, at which the new assembly line produces these components?

$\frac{3B}{h}$ Answer
B
$\frac{B}{3h}$
C
$\frac{3h}{B}$
D
$3Bh$
E
$\frac{h}{3B}$

Answer

The expression

\frac{3B}{h}

represents the rate of production of the new assembly line.

The correct answer shows that the rate of production is the number of components divided by the new time, which is one-third of the original time. Since the original time is

h

hours, the new time is

\frac{h}{3}

hours. Dividing the number of components

B

\frac{h}{3}

yields

B \div \frac{h}{3} = B \times \frac{3}{h} = \frac{3B}{h}

components per hour.

Step-by-Step Solution

Determine the time it takes for the new assembly line to produce the batch of components.

The new assembly line takes

\frac{h}{3}

hours.

The problem states the new line produces the batch in

\frac{1}{3}

of the original time,

h

Set up the algebraic expression for the rate of production in components per hour.

\text{Rate} = \frac{\text{Total Components}}{\text{Total Time}} = \frac{B}{\frac{h}{3}}

Rate is defined as quantity produced divided by time elapsed.

Simplify the fraction to find the final expression.

\text{Rate} = B \times \frac{3}{h} = \frac{3B}{h}

Dividing by a fraction is equivalent to multiplying by its reciprocal.

Key Concept

Formulating algebraic rate expressions from word problems

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic