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Chapter 7: Problem 35

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.

Short Answer

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

Step by step solution

01

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.
02

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.
03

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.

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Most popular questions from this chapter

perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\text { Simplify: } \frac{(y+2) y-2 \cdot 4}{4 y(y+4)}$$

add or subtract as indicated. Simplify the result, if possible. $$\frac{3 y^{2}-2}{3 y^{2}+10 y-8}-\frac{y+10}{3 y^{2}+10 y-8}-\frac{y^{2}-6 y}{3 y^{2}+10 y-8}$$

Anthropologists and forensic scientists classify skulls using $$ \frac{L+60 W}{L}-\frac{L-40 W}{L} $$ where \(L\) is the skull's length and \(W\) is its width. a. Express the classification as a single rational expression. b. If the value of the rational expression in part (a) is less than \(75,\) a skull is classified as long. A medium skull has a value between 75 and \(80,\) and a round skull has a value over \(80 .\) Use your rational expression from part (a) to classify a skull that is 5 inches wide and 6 inches long.

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I can clean my house in 3 hours and my sloppy friend can completely mess it up in 6 hours, so if we both "work" together, the time, \(x,\) it takes to clean the house can be modeled by \(\frac{x}{3}-\frac{x}{6}=1\)

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{x}{x-y}+\frac{y}{y-x}$$
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