Math Problem Statement

A gas bottle contains 50 L of liquid gas. If the liquid gas is used at a rate of 20 mL per minute, how many hours will the gas bottle last?

Solution

The question provided asks:

"A gas bottle contains 50 L of liquid gas. If the liquid gas is used at a rate of 20 mL per minute, how many hours will the gas bottle last?"

Step-by-step solution:

  1. Convert 50 L to milliliters (mL): Since 1 liter (L) = 1000 milliliters (mL), we can convert: 50L=50×1000=50,000mL50 \, \text{L} = 50 \times 1000 = 50,000 \, \text{mL}

  2. Calculate the time in minutes: The gas is being used at a rate of 20 mL per minute. To find out how long it will last, we divide the total volume by the rate of use: Time in minutes=50,000mL20mL/min=2,500minutes\text{Time in minutes} = \frac{50,000 \, \text{mL}}{20 \, \text{mL/min}} = 2,500 \, \text{minutes}

  3. Convert minutes to hours: Since there are 60 minutes in an hour, we convert the time to hours: Time in hours=2,500minutes60=41.67hours\text{Time in hours} = \frac{2,500 \, \text{minutes}}{60} = 41.67 \, \text{hours}

Final Answer:

The gas bottle will last for 41.67 hours, or approximately 41 hours and 40 minutes.

Let me know if you'd like any further explanation or have questions. Here are some related questions to deepen your understanding:

  1. If the rate of usage increased to 50 mL per minute, how long would the gas last?
  2. How would the result change if the bottle had 100 liters of liquid gas instead?
  3. If the rate of gas usage varies, how can we calculate the total duration of usage?
  4. How much gas will be consumed in 5 hours at the same rate of 20 mL per minute?
  5. How can we model the consumption over time using a graph?

Tip: Always ensure unit consistency when solving word problems to avoid calculation errors.

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Math Problem Analysis

Mathematical Concepts

Unit Conversion
Rate of Usage
Time Calculation

Formulas

Volume conversion: 1 liter = 1000 milliliters
Time in minutes = Total volume / Rate of usage
Time in hours = Time in minutes / 60

Theorems

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Suitable Grade Level

Grades 6-8