Rate Problems: Plugging in Rate Problems - Work as an Invisible Variable

Working together, Joe and Joanne finish a job in 2 hours. How long will it take Jeremy and Joe to finish the job? >(1) Working alone and without breaks, Joe takes 5 hours to finish the job. This is 400% as long as it takes Jeremy to finish the job. >(2) Working alone and without breaks, Joanne takes 10 hours to finish the job three times.

For Stat. (2), you can place the information in a rate box, but at the end of the day, Stat. (2) tells you nothing about Jeremy's rate; it only tells you about Joanne's (and possible Joe's) rate. Without Jeremy's rate, there's no way to find the combined rate of Joe and Jeremy. Therefore, **Stat.(2) → IS → A**.

Stat. (1) tells you that it takes 5 hours for Joe to finish the job. Create a row for Joe and add this information. In addition, it says that 5 hours is 400% of (or four times) the time it takes Jeremy to finish the work. Therefore, $$5 = 4J$$, so $$J=\frac{5}{4}$$. Place this information into the rate box and use it to calculate the rates for Joe and Jeremy: | | RATE | TIME | WORK | |--------------|--------------------------------------------------------|-------------------------------|------| | Joe + Joanne | $$\frac{10}{2}=5$$ | $$2$$ | $$10$$ | | Joe + Jeremy | | {color:red}$$?$${/color} | $$10$$ | | Joe | $$\color{blue}{\frac{10}{5}=2}$$ | $$5$$ | $$10$$ | | Jeremy | $$\color{blue}{\dfrac{10}{\frac{5}{4}}=8}$$ | $$\frac{5}{4}$$ | $$10$$ | Once you have Joe and Jeremy's individual rates, you can find their combined rate and then find the time it will take them both to finish the job. **Stat.(1) → S → AD**.

Incorrect. [[snippet]] For Stat. (2), you can place the information in a rate box, but at the end of the day, Stat. (2) tells you nothing about Jeremy's rate; it only tells you about Joanne's (and possible Joe's) rate. Without Jeremy's rate, there's no way to find the combined rate of Joe and Jeremy. Therefore, **Stat.(2) → IS → ACE**.

Correct. [[snippet]] Once you have set up the rate box for the stem, go to the statements.

Incorrect. [[snippet]] Once you have set up the rate box for the stem, go to the statements.

Incorrect. [[snippet]] Not only is there sufficient data to answer the question, but you do not even need to combine both statements for that purpose.

Statement (1) ALONE is sufficient, but Statement (2) alone is not sufficient to answer the question asked.

Statement (2) ALONE is sufficient, but Statement (1) alone is not sufficient to answer the question asked.

BOTH Statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

EACH statement ALONE is sufficient to answer the question asked.

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

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Rate Problems: Plugging in Rate Problems - Work as an Invisible Variable

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