Question 94·Easy·Linear Equations in One Variable
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?
For constant-rate word problems, first decide whether the question is about how much has been drained or how much remains. Subtract to find the amount of change, then use the basic relationship to set up a one-variable linear equation. Solve by isolating the variable with inverse operations (usually one division), and finally plug your answer back into the situation (or quickly multiply rate by time and subtract) to confirm it gives the requested final amount.
Hints
Compare the starting and ending amounts
First, find how many liters of water must be drained by subtracting the final amount (3,120 liters) from the initial amount (5,200 liters).
Connect drained water to rate and time
Once you know how many liters are drained, think about how to use the constant rate of 160 liters per hour to find the time. What equation relates rate, time, and amount drained?
Solve the equation carefully
Your equation should have the form . Divide both sides by 160 to solve for , the time in hours.
Desmos Guide
Calculate the total amount drained
In a Desmos expression line, type 5200-3120 and press Enter. The result shown is the total number of liters that must be drained from the tank.
Divide by the draining rate
In a new expression line, type (5200-3120)/160. The value Desmos displays is the time in hours it takes to drain the tank down to 3,120 liters at 160 liters per hour.
Step-by-step Explanation
Find how much water is drained
The tank starts with 5,200 liters and should end with 3,120 liters.
Compute how much water must be removed:
So, 2,080 liters of water need to be drained from the tank.
Relate drained water to rate and time
The pump drains water at a constant rate of 160 liters per hour.
Use the relationship
Let be the time in hours. Then
Solve the equation for time
To find , solve the equation by dividing both sides by 160:
Now you just need to compute this division.
Compute the quotient and choose the answer
Simplify by dividing numerator and denominator by 10:
Now notice that , so
Therefore, it will take hours for the amount of water in the tank to reach 3,120 liters. The correct answer is C) 13.