A digital commercial printing press operates at a constant rate of r pages per minute. Dur… — ACT

A digital commercial printing press operates at a constant rate of $r$ pages per minute. During a scheduled production session lasting $t$ minutes, the machine was paused for $12$ minutes due to paper replenishment. If the printing press successfully printed $p$ pages during the operational portion of the session, which of the following equations correctly expresses the relationship between $r$ , $p$ , and $t$ ?

A
$r = \frac{p}{t} - 12$
$r = \frac{p}{t - 12}$ Answer
C
$r = \frac{p}{t + 12}$
D
$r = \frac{p - 12}{t}$
E
$r = \frac{12p}{t}$

Answer

The correct equation is

r = \frac{p}{t - 12}

Since the press was paused for 12 minutes during a session of

t

minutes, the total time spent actually printing was

(t - 12)

minutes. The printing rate

r

is defined as pages printed divided by active printing time, giving

r = \frac{p}{t - 12}

Step-by-Step Solution

Identify the active printing time in terms of

t

Active operating time =

(t - 12)

minutes.

The machine was paused for 12 minutes out of the total session duration of

t

minutes.

Use the basic rate relationship Rate = Quantity / Time.

r = \frac{p}{t - 12}

Dividing the total pages printed

p

by the active printing duration

(t - 12)

yields the rate

r

in pages per minute.

Key Concept

Formulating one-step rate and time algebraic relationships with adjusted variables.

Question

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