Question

A town has a water treatment plant but decides to build a second, more efficient facility. The new treatment plant can filter the water in the reservoir four times as quickly as the older facility. If they work together, they can purify the whole water in the reservoir in $72$ hrs. The equation represents the scenario: Which of the following describes what the term $\frac{1}{x}$ represents?
$\frac{1}{x}+\frac{4}{x}=\frac{1}{72}$

• A. The portion of the water the older treatment plant can filter in 1 hour
• B. The time it takes the older treatment plant to 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

Answer 1

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

Since the two plants when combined, can purify the water in $72$ hours, $\frac{1}{72}$ shows the portion of water that the two plants would purify in $1$ hour.

$\frac{1}{x}+\frac{4}{x}$ thus shows the portion of water that can be purified by the respective older and newer tanks to add up to $\frac{1}{72}$

Thus, $\frac{1}{x}$ shows the portion of water that the older treatment plant can purify in $1$ hour and $4$ being multiplied shows that the newer plant works $4$ times faster than the older plant.