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
30 and three fourths
miles in 41 minutes.
(Simplify your answer. Type an integer, proper fraction, or mixed number.)
Part 2
The car will travel
enter your response here miles in 1 hour.
(Simplify your answer. Type an integer, proper fraction, or mixed number.)
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
30 and three fourths
miles in 41 minutes.
(Simplify your answer. Type an integer, proper fraction, or mixed number.)
Part 2
The car will travel
enter your response here miles in 1 hour.
(Simplify your answer. Type an integer, proper fraction, or mixed number.)
Answers
GPT-4o mini
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
1. **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.
2. **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:
\[
\text{Distance in 41 minutes} = \text{Speed} \times \text{Time} = \frac{3}{4} \text{ miles per minute} \times 41 \text{ minutes} = \frac{3 \times 41}{4} = \frac{123}{4}.
\]
3. **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.
### Part 1: Find the speed of the car
1. **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.
2. **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:
\[
\text{Distance in 41 minutes} = \text{Speed} \times \text{Time} = \frac{3}{4} \text{ miles per minute} \times 41 \text{ minutes} = \frac{3 \times 41}{4} = \frac{123}{4}.
\]
3. **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.