Problem 34 - Introductory Algebra for College Students

Question

If you know how many hours it takes for you to do a job, explain how to find the fractional part of the job you can complete in \(x\) hours.

Step-by-Step Solution

Answer

The fraction of the job that can be completed in \(x\) hours is \(\frac{x}{T}\), where \(T\) is the total hours needed to complete the job.

Step 1: Define the Known Variables

First, gather the needed information. Let's denote the total hours needed to complete the task as \(T\) hours. The duration for which we want to find out the fraction of the job completed is \(x\) hours.

Step 2: Create a Ratio

Next, based on the given quantities, a ratio can be created. This ratio will represent the fraction of the job completed in \(x\) hours. Formally, this is written as \(\frac{x}{T}\).

Step 3: Interpret the Ratio

Finally, interpret this ratio. \(\frac{x}{T}\) tells us the portion of the job that can be completed in \(x\) hours. The result is a fraction, so if \(\frac{x}{T} = \frac{1}{2}\), this means half of the job can be completed in \(x\) hours. If \(\frac{x}{T} = 1\), you will complete the entire job in \(x\) hours.