To solve the problem, we first need to determine the car's speed in miles per minute, and then use that speed to find out how far it travels in 41 minutes and in 1 hour.
Part 1: Find the speed of the car
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Convert the distance and time into improper fractions:
- Distance: \(2 \frac{1}{2}\) miles = \(2 + \frac{1}{2} = \frac{5}{2}\) miles.
- Time: \(3 \frac{1}{3}\) minutes = \(3 + \frac{1}{3} = \frac{10}{3}\) minutes.
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Calculate the speed (miles per minute): \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{\frac{5}{2}}{\frac{10}{3}} = \frac{5}{2} \times \frac{3}{10} = \frac{15}{20} = \frac{3}{4} \text{ miles per minute}. \]
Part 2: Calculate the distance traveled in 41 minutes
Now, using the speed, we can calculate the distance traveled in 41 minutes:
\[ \text{Distance in 41 minutes} = \text{Speed} \times \text{Time} = \frac{3}{4} \text{ miles per minute} \times 41 \text{ minutes} = \frac{3 \times 41}{4} = \frac{123}{4}. \]
- Convert \( \frac{123}{4} \) to a mixed number:
- \(123 \div 4 = 30\) with a remainder of \(3\), so: \[ \frac{123}{4} = 30 \frac{3}{4}. \]
So, in 41 minutes, the car will travel \(30 \frac{3}{4}\) miles.
Part 3: Calculate the distance traveled in 1 hour
1 hour is 60 minutes. Using the same speed:
\[ \text{Distance in 1 hour} = \frac{3}{4} \text{ miles per minute} \times 60 \text{ minutes} = \frac{3 \times 60}{4} = \frac{180}{4} = 45 \text{ miles}. \]
Final Answers:
- The car will travel 30 and three fourths miles in 41 minutes.
- The car will travel 45 miles in 1 hour.
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