Problem 35 - Introductory Algebra for College Students

Question

If you can do a job in 6 hours and your friend can do the same job in 3 hours, explain how to find how long it takes to complete the job working together. It is not necessary to solve the problem.

Step-by-Step Solution

Answer

It would take 2 hours for both individuals, when working together, to complete the job.

Step 1: Determine Individual Rates of Work

The first step is to determine the rates at which both you and your friend can individually do the job. This can be calculated by dividing 1 by the number of hours each of you take. If the job takes you 6 hours to complete, your rate of work is \(\frac{1}{6}\) job per hour. And if your friend completes the work in 3 hours, his rate of work is \(\frac{1}{3}\) job per hour.

Step 2: Add Rates of Work Together

In the second step, simply add the rates of work together. This will give the combined rate at which you can both do the job together. So, add \(\frac{1}{6}\) job per hour (your rate) and \(\frac{1}{3}\) job per hour (your friend's rate) to get \(\frac{1}{6} + \frac{1}{3} = \frac{1}{2}\) job per hour.

Step 3: Calculate Time Taken Together

In the third step, to find out how long it takes for both of you to finish the job together, simply take the reciprocal of the sum of rates which is the derived combined rate, i.e., \(\frac{1}{ \frac{1}{2} } = 2\) hours. This is the time it would take for both of you, working together, to complete the job.