Question

$\frac{1}{x}+\frac{4}{x}=\frac{1}{72}$
In order to create safe drinking water, cities and towns use water treatment facilities to remove contaminate from surface water and groundwater. Suppose a town has a treatment plant but decides to build a second, more efficient facility. The new treatment plant can filter as the older facility. Working together, the two facilities can filter all the water in the reservoir in 72 hours. The equation above represents the scenario. Which of the following describes what the term $\frac{1}{x}$ represents?

• A. The portion of the water the older treatment plant can filter in 1 hour
• B. The time it takes the older treatment plant of filter the water in the reservoir
• C. The time it takes the older treatment plant to filter $\frac{1}{72}$ of the water in the reservoir
• D. The portion of the water the new treatment plant can filter in 4 hours

Answer 1

The correct option is A The portion of the water the older treatment plant can filter in 1 hour

$\Rightarrow$ The rate given in the question in terms of the constant term you see on the right-hand side of the equation. Working together, the two treatment plants can filter the water in $72$ hours. This is equivalent to saying that they can filter $\frac{1}{72}$ of the water in $1$ hour.

$\Rightarrow$ If $\frac{1}{72}$ is the portion of the water the two treatment plants can filter together, then each term on the left side of the equation represents the portion that each plant can filter individually in $1$ hour.

$\Rightarrow$ Because the new facility is $4$ times as fast as the older facility, represents the portion of the water the new plant can filter in $1$ hour, and represents the portion of the water the older plant can filter in $1$ hour.