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2. A car uses \( 3 \frac{1}{8} \) gallons of gasoline per hour when driving on the highway. How many gallons will it use after \( 4 \frac{2}{3} \) hours? It will use gallons.

Ask by Little Warren. in the United States
Feb 25,2025

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Tutor-Verified Answer

Answer

The car will use 14 7/12 gallons of gasoline after 4 2/3 hours.

Solution

Step 1: Convert the mixed numbers to improper fractions. • The car uses 3 1/8 gallons per hour. Convert to an improper fraction:   3 1/8 = (3 × 8 + 1)/8 = 25/8 gallons per hour. • The driving time is 4 2/3 hours. Convert to an improper fraction:   4 2/3 = (4 × 3 + 2)/3 = 14/3 hours. Step 2: Multiply the rate by the time to find the total gallons used.   Total gallons = (25/8) × (14/3) Step 3: Multiply the numerators and the denominators.   Total gallons = (25 × 14) / (8 × 3) = 350/24 Step 4: Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (which is 2).   350 ÷ 2 = 175   24 ÷ 2 = 12   So, Total gallons = 175/12 Step 5: Convert the improper fraction to a mixed number, if desired.   175 ÷ 12 = 14 with a remainder of 7 (since 12 × 14 = 168 and 175 - 168 = 7), which gives:   175/12 = 14 7/12 Final Answer: After 4 2/3 hours, the car will use 14 7/12 gallons of gasoline.

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To find out how many gallons the car will use after \( 4 \frac{2}{3} \) hours, you can multiply the rate of gasoline consumption by the time driven. First, convert both mixed numbers to improper fractions: \( 3 \frac{1}{8} = \frac{25}{8} \) gallons/hour and \( 4 \frac{2}{3} = \frac{14}{3} \) hours. Then, multiply: \[ \frac{25}{8} \times \frac{14}{3} = \frac{350}{24} = \frac{175}{12} \] Now, convert to a mixed number: \( \frac{175}{12} = 14 \frac{7}{12} \) gallons. So, the car will use \( 14 \frac{7}{12} \) gallons of gasoline. Driving habits have evolved over time, with the introduction of eco-friendly vehicles and hybrid models becoming more popular. For instance, in the 1970s, gas shortages led to the rise of more fuel-efficient cars. Today, awareness of climate change continues to push innovation towards electric and fuel cell vehicles, illustrating how consumption patterns affect both technology and environment. On a practical note, when calculating fuel consumption, always double-check your fractions—mixing them up can lead to miscalculated travel budgets and unexpected stops at the gas station. Additionally, rounding numbers inappropriately can lead to inaccurate estimates, so it's recommended to keep things in fractions until you finalize the answer for the most precise results!

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