Solve for t.
d = rt
The problem asks us to solve for the variable \(t\) given the linear equation \(d = rt\), where \(d, r,\) and \(t\) represent variables (such as distance, rate, and time). Our goal is to isolate \(t\) on one side of the equation. This is a basic algebraic manipulation problem where we apply operations to both sides of the equation to maintain equality.
To isolate \(t\), we need to eliminate the factor of \(r\) from the right-hand side of the equation. Since \(r\) is multiplied by \(t\), the inverse operation is division. We divide both sides of the equation \(d = rt\) by \(r\), assuming \(r
eq 0\):
\[\frac{d}{r} = \frac{rt}{r}\]
Simplifying the right side, we get:
\[\frac{d}{r} = t\]
Thus, the expression for \(t\) is \(t = \frac{d}{r}\). This corresponds to the third option provided.
In physics and everyday life, the relationship between distance (\(d\)), rate or speed (\(r\)), and time (\(t\)) is fundamental. For example, if you know you need to travel a distance of \(100\) miles at a constant speed of \(50\) miles per hour, you can use the formula \(t = \frac{d}{r}\) to calculate the time required: \(t = \frac{100}{50} = 2\) hours. This simple rearrangement allows you to plan travel times, predict when a task will be completed, or understand the relationship between speed and duration.