Question 466·Easy·Algebra

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A storage tank contains 5,200 liters of water. A pump drains the water at a constant rate of 160 liters per hour. At this rate, after how many hours will exactly 3,120 liters of water remain in the tank?

A pump draining at a constant rate calls for a linear model: the tank loses the same number of liters each hour. Subtract the amount drained from the starting amount, then set that equal to the amount left. Use a Desmos regression to find the time. The key trap is treating the water remaining as the water drained.

Hints

Hint 1
A rate of $160$ liters per hour means the pump removes $160$ liters in each hour. If $h$ is the number of hours, how many liters has it removed?
Hint 2
The tank starts with more water than it ends with. Use starting amount minus amount drained to describe the water remaining, then set that expression equal to $3{,}120$ liters.

Step-by-step

Model the water remaining
Step 1
Write the remaining-water equation
Let $h$ be the number of hours. At $160$ liters per hour, the pump drains $160h$ liters in $h$ hours. Starting amount minus amount drained equals amount remaining, so $5{,}200-160h=3{,}120$ . The $3{,}120$ liters remain; they aren't the amount the pump removed.
Step 2
Solve for the time in Desmos
Type $5200-160x_1\sim3120$ . Replace $h$ with $x_1$ because Desmos uses $x_1$ for an unknown it can find; $\sim$ tells it to make the two sides equal. Desmos reports $x_1=13$ under PARAMETERS, so exactly $3{,}120$ liters remain after 13 hours. Choice C.

Question 466·Easy·Algebra

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