A barrel contains 177 gallons of paint and is being drained at a constant rate of 14 gallons per minute. Write an equation that models the number of gallons, g, after t minutes.
A barrel contains 177 gallons of paint and is being drained at a constant rate of 14 gallons per minute. Write an equation that models the number of gallons, g, after t minutes.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Modeling Draining of a Barrel of Paint
A barrel contains 177 gallons of paint and is being drained at a constant rate of 14 gallons per minute.
**Question**: Write an equation that models the number of gallons, \( g \), after \( t \) minutes.
**Solution**:
To model the situation, we need to consider the initial amount of paint and the rate at which it is being drained.
1. **Initial amount of paint**: 177 gallons.
2. **Rate of drainage**: 14 gallons per minute.
Let's denote:
- \( g \) as the number of gallons of paint remaining in the barrel.
- \( t \) as the time in minutes.
The equation will take the form of:
\[ g = \text{initial amount} - (\text{drainage rate} \times \text{time}) \]
Plugging in the given values:
\[ g = 177 - 14t \]
Therefore, the equation that models the given situation is:
\[ g = 177 - 14t \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F375a8daa-a061-40df-aa13-f324a3b06fab%2Fe79bc8db-deeb-4342-bb09-7f1e677dbf52%2Ftypboxh_processed.png&w=3840&q=75)
Transcribed Image Text:### Modeling Draining of a Barrel of Paint
A barrel contains 177 gallons of paint and is being drained at a constant rate of 14 gallons per minute.
**Question**: Write an equation that models the number of gallons, \( g \), after \( t \) minutes.
**Solution**:
To model the situation, we need to consider the initial amount of paint and the rate at which it is being drained.
1. **Initial amount of paint**: 177 gallons.
2. **Rate of drainage**: 14 gallons per minute.
Let's denote:
- \( g \) as the number of gallons of paint remaining in the barrel.
- \( t \) as the time in minutes.
The equation will take the form of:
\[ g = \text{initial amount} - (\text{drainage rate} \times \text{time}) \]
Plugging in the given values:
\[ g = 177 - 14t \]
Therefore, the equation that models the given situation is:
\[ g = 177 - 14t \]
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