Problem 7 - Prealgebra

Question

Express each of the following rates as a ratio with the given units. Liters/Minute It takes 4 minutes to fill a 56 -liter gas tank. What is the rate in liters per minute?

Step-by-Step Solution

Answer

14 liters per minute.

Step 1: Understand the Problem

We need to express the rate of filling a gas tank in terms of liters per minute. Here we have 4 minutes to fill up a 56-liter gas tank.

Step 2: Calculate the Rate

To find the rate, divide the total volume by the time it takes. So, the rate is calculated as \( \text{Rate} = \frac{56 \text{ liters}}{4 \text{ minutes}} \).

Step 3: Simplify the Expression

Perform the division: \( \frac{56}{4} = 14 \). Therefore, the rate is 14 liters per minute.

Key Concepts

Understanding Rates

In everyday life, rates tell us how one quantity changes in relation to another over time. In this example, the rate we're discussing is how quickly a gas tank fills with gasoline. When we say "liters per minute," we're describing how many liters of gasoline are being added to the tank every single minute. To calculate the rate, we divide the total number of liters by the total number of minutes.

• If you fill a 56-liter tank in 4 minutes, the calculation of the rate would be: \( \frac{56 \text{ liters}}{4 \text{ minutes}} \).
• This results in 14 liters per minute, meaning 14 liters are pumped into the tank every minute.
• Expressing it this way helps us quickly understand the speed of the filling process.

Rates are a foundational concept in math and science, helping us measure and compare the efficiency of different processes.

Unit Conversion Techniques

Unit conversion is essential when working with rates, as it allows us to express measurements in the most useful form for the situation. In our exercise, the given rate was already conveniently in liters per minute. However, suppose you need to convert the unit to something else, like gallons per minute. You would need to know that:

• 1 liter is approximately equal to 0.264 gallons.
• To convert 14 liters to gallons, you multiply: \( 14 \times 0.264 \text{ gallons per liter} \).
• This results in approximately 3.696 gallons per minute.

Understanding how to perform these conversions ensures that you can communicate measurements effectively across different systems of measurement, enabling clear and accurate comparisons or calculations.

Solving Word Problems

Word problems can sometimes seem challenging, but breaking them down into simple steps can make them much easier to tackle. Let's outline how to approach solving word problems like the one in the exercise:

• Identify the known quantities: Start by determining what information you have. In our exercise, we know the tank size (56 liters) and the time (4 minutes).
• Identify what you need to find: We need the rate in liters per minute.
• Set up the relationship: Use the formula for rate, which is quantity over time. Here, it’s \( \frac{56 \text{ liters}}{4 \text{ minutes}} \).
• Perform the calculations: Simplify the fraction to find the rate – in this case, 14 liters per minute.
• Verify your solution: Double-check calculations to ensure accuracy.

By following these steps, you can systematically solve most word problems with confidence.