Challenge A car is traveling at a steady speed. It travels 2 and one half

Question

miles in 3 and one third
minutes. How far will it travel in 41 minutes​? In 1 hour​?
Question content area bottom
Part 1
The car will travel
  
enter your response here miles in 41 minutes.
​(Simplify your answer. Type an​ integer, proper​ fraction, or mixed​ number.)

Answer 1

To find out how far the car will travel in 41 minutes, we first need to determine the car's speed in miles per minute based on the information given.

1. Convert the distances and times to improper fractions:

   • Distance traveled: \(2 \frac{1}{2} = \frac{5}{2} \text{ miles}\)
   • Time taken: \(3 \frac{1}{3} = \frac{10}{3} \text{ minutes}\)

2. Calculate the speed in miles per minute: To find the speed, divide the distance by the time: \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{\frac{5}{2}}{\frac{10}{3}} = \frac{5}{2} \times \frac{3}{10} = \frac{15}{20} = \frac{3}{4} \text{ miles per minute} \]

3. Calculate the distance traveled in 41 minutes: Now, to find out how far the car travels in 41 minutes: \[ \text{Distance} = \text{Speed} \times \text{Time} = \frac{3}{4} \text{ miles per minute} \times 41 \text{ minutes} = \frac{3 \times 41}{4} = \frac{123}{4} \] Convert \(\frac{123}{4}\) to a mixed number: \[ \frac{123}{4} = 30 \frac{3}{4} \text{ miles} \]

Therefore, the car will travel \(30 \frac{3}{4}\) miles in 41 minutes.

Final Answer: The car will travel \(30 \frac{3}{4}\) miles in 41 minutes.