91Ó°ÊÓ

When using the Distance-Rate-Time formula, it's essential to understand how to isolate a specific variable. This allows us to find the value of one unknown if we know the others. Here, our equation is \(d = rt\). We need to solve for \(t\). To do this, follow these steps:

- Identify the variable you need to isolate (in this case, \(t\)).
- Move the other variables to the opposite side of the equation.

Since \(t\) is being multiplied by \(r\), we can divide both sides of the equation by \(r\): \[ t = \frac{d}{r} \] And that's how we've isolated \(t\)! Now, you can find \(t\) if you know \(d\) and \(r\). This process of isolating the variable is a foundational skill in algebra, used in many different types of equations.

Substitution is a powerful algebraic technique that allows us to replace variables with their known values. This reduces the complexity of the equation, letting us solve it more easily. Let's look at our example:

- We have the equation \[ t = \frac{d}{r} \]
- To find \(t\) when \(d=350\) and \(r=70\), we substitute these values into the equation: \[ t = \frac{350}{70} \]
By plugging in these numbers, we convert our abstract formula into a more concrete calculation. Substitution simplifies the problem and brings us one step closer to finding the solution.

Simplifying fractions is a crucial skill for solving many math problems, including this exercise. Simplifying a fraction means reducing it to its simplest form, where the numerator and denominator are as small as possible. Here's how we do it for our example:

- We have the fraction \[ \frac{350}{70} \]
- To simplify, find the greatest common divisor (GCD) of the numerator and denominator. For 350 and 70, the GCD is 70.
- Divide both the numerator and the denominator by their GCD: \[ \frac{350 ÷ 70}{70 ÷ 70} = \frac{5}{1} = 5 \]
And there you have it! The simplified fraction is 5. Simplifying fractions can make calculations easier and the results clearer. In our problem, simplifying \( \frac{350}{70} \) shows us that \( t = 5 \).