Problem 88 - Introductory Algebra for College Students

Question

Will help you prepare for the material covered in the next section. If you can complete a job in 5 hours, what fractional part of the job can you complete in 1 hour? in 3 hours? in \(x\) hours?

Step-by-Step Solution

Answer

In 1 hour, \(1/5\) of the job can be done. In 3 hours, \(3/5\) of the job can be done. In \(x\) hours, \(x/5\) of the job can be done.

Step 1: Calculate Fraction for 1 Hour

Since a full job takes 5 hours to complete, in one hour only a 1/5 fraction of the job will be completed. As such, the unit is divided by the total hours needed to achieve the task, hence \(1/5\).

Step 2: Calculate Fraction for 3 Hours

Again, the same logic applies for 3 hours. The task completion is proportionate to the time spent on it, compared to the total 5 hours needed. Hence, 3 hours would mean \(3/5\) of the task was completed.

Step 3: Calculate Fraction for x Hours

The same principle applies when determining the fraction of the job completed in x hours. Therefore, if x hours are spent on the job, \(x/5\) of it is completed. Please note that, the value for x should be within the bounds of the total time taken, i.e., 0 <= x <= 5. Beyond these bounds, the calculation will not make sense as it would mean that x exceeds the total time needed to complete the job or is less than no time spent on the job.