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Chapter 2: Problem 67

Solve each formula for the specified variable. \(d=r t\) for \(t\)

Short Answer

Expert verified
The solution for \(t\) is \(t = \frac{d}{r}\).

Step by step solution

01

- Identify the given formula

The given formula is \(d = r \, t\). This formula represents the relationship between distance (\(d\)), rate (\(r\)), and time (\(t\)).
02

- Isolate the specified variable

In this case, we need to solve for \(t\). To do that, isolate \(t\) on one side of the equation. Divide both sides of the equation by \(r\) so that \(t\) is alone: \(t = \frac{d}{r}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

algebra
Algebra is the branch of mathematics that deals with symbols and the rules for manipulating those symbols.
These symbols represent quantities without fixed values, known as variables.
The basic operations of algebra include addition, subtraction, multiplication, and division.
Understanding these operations is essential for solving equations and manipulating variables.
In algebra, we often work with formulas, which express relationships between different variables. For example, the formula from our exercise, \(d = r \, t\), connects distance (\(d\)), rate (\(r\)), and time (\(t\)). They indicate how changing one variable affects the others.
equation manipulation
Equation manipulation involves altering an equation to solve for a specific variable.
In our example, we start with the formula \(d = r \, t\) and need to solve for \(t\).
Here's how we can do it step-by-step:
  • Identify the equation: \(d = r \, t\)

  • Determine which variable to isolate. In this case, it's \(t\).

  • To solve for \(t\), we need to isolate it on one side of the equation. We do this by dividing both sides by \(r\).

So our calculation becomes:
\[ t = \frac{d}{r} \] By performing these steps, we've manipulated the original equation to solve for the specific variable \(t\).
formulas
Formulas are equations that express relationships between different variables.
They help us understand how changing one quantity affects another.
For example, the formula \(d = r \, t\) links distance (\(d\)), rate (\(r\)), and time (\(t\)).
When working with formulas, it's important to understand which variables are given and which ones you need to find.
  • Identify the formula.

  • Determine the knowns and the unknowns.

  • Isolate the variable you need to solve.

By following these steps, you can effectively use and manipulate formulas in algebra to find the unknown values.

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