Question

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