Question

You can solve the formula \(d=r t\) for any of its variables. This means that you need to learn only one formula to solve a problem asking for distance, rate, or time. Explain.

Short answer

The formula \(d = rt\) relates distance, rate, and time. By manipulating this formula, any of these variables can be calculated if the other two are known. Specifically, to calculate rate, use \(r = d / t\) and to calculate time, use \(t = d / r\). So, understanding this one formula allows you to solve problems asking for distance, rate, or time.

Step-by-step solution

Understanding the formula

The formula \(d = rt\) can be understood as follows: the distance (d) that an object travels is equal to its rate or speed (r) multiplied by the time (t) it travels for.

Solving for 'r' (rate)

In order to solve the formula for rate, we need to isolate 'r' on one side of the equation. Knowing that multiplication is the inverse of division, we can write the formula for 'r' as \(r = d / t\).

Solving for 't' (time)

Similarly, if we need to calculate the time, we can express 't' by isolating it on one side of the equation. Here, we use the same principle, but now divide distance by rate, which gives \(t = d / r\)