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Question

Difficulty: EasyInterpreting Linear Relationships in Context

A scientist is monitoring the volume of liquid nitrogen in a storage tank. The volume VV, in liters, of liquid nitrogen remaining in the tank tt hours after a cooling system malfunction is modeled by the equation V=240−1.5tV = 240 - 1.5t. After how many hours of malfunction will there be exactly 180180 liters of liquid nitrogen remaining in the tank?

Answer: 40 hours

Answer

The cooling system malfunction must last 40 hours for there to be exactly 180 liters of liquid nitrogen remaining in the tank.
To find the number of hours of malfunction until 180180 liters of liquid nitrogen remain in the tank, substitute 180180 for VV in the given model equation, yielding 180=240−1.5t180 = 240 - 1.5t. Subtracting 240240 from both sides of the equation results in −60=−1.5t-60 = -1.5t. Dividing both sides by −1.5-1.5 gives the final value of t=40t = 40 hours.

Step-by-Step Solution

1
Substitute the target volume of liquid nitrogen into the linear equation.
180=240−1.5t180 = 240 - 1.5t
The question asks for the time tt when the remaining volume VV is exactly 180180 liters.
2
Isolate the term containing the variable by subtracting the initial constant volume from both sides.
−60=−1.5t-60 = -1.5t
Subtracting 240240 from both sides of the equation begins the process of isolating the variable tt.
3
Divide both sides of the equation by the rate coefficient to solve for time.
t=40t = 40
Dividing by −1.5-1.5 isolates the variable tt and gives the solution in hours.

Key Concept

Interpreting values and solving equations in linear contexts
Estimated Time:45s
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Topics

Interpreting Linear Relationships in Context

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