A runner completed a race in 45 minutes. If this time is 12 minutes faster than their prev… — ACT

A runner completed a race in $45$ minutes. If this time is $12$ minutes faster than their previous race time, $t$ , which of the following equations can be used to find the previous race time?

$t - 12 = 45$ Answer
B
$t + 12 = 45$
C
$12 - t = 45$
D
$12t = 45$
E
$\frac{t}{12} = 45$

Answer

The equation

t - 12 = 45

correctly models the relationship between the previous and current race times.

The equation

t - 12 = 45

is correct because 'faster than' in running means a shorter duration of time. Thus, the previous time

t

must be

12

minutes greater than

45

minutes, which is algebraically expressed as

t - 12 = 45

(or

t = 45 + 12

Step-by-Step Solution

Identify the relationship between the current time and the previous time

t

The current time is

45

minutes, which is

12

minutes faster than

t

This establishes that the previous time

t

is larger than the current time of

45

minutes.

Set up the algebraic equation based on the time difference.

t - 12 = 45

Subtracting the difference of

12

minutes from the slower previous time

t

yields the faster current time of

45

minutes.

Key Concept

Translating verbal descriptions of differences into one-step subtraction equations

Estimated Time:45s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

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