An airline company purchased two new airplanes. One can travel at speeds of up to 600 miles per hour and the other at speeds of up to 720 miles per hour. How many more miles can the faster airplane travel in 12 seconds than the slower airplane?

Options

A. `(1)/(30)`
B. `(2)/(5)`
C. `2`
D. `30`

Answer

To solve the problem, we need to find out how many more miles the faster airplane can travel in 12 seconds compared to the slower airplane.

### Step-by-Step Solution:

1. **Determine the speed of each airplane:**
- The slower airplane travels at 600 miles per hour.
- The faster airplane travels at 720 miles per hour.

2. **Convert the speed from miles per hour to miles per second:**
- There are 3600 seconds in an hour (60 minutes × 60 seconds).
- For the slower airplane:
\[ \text{Speed in miles per second} = \frac{600 \text{ miles}}{3600 \text{ seconds}} = \frac{600}{3600} = \frac{1}{6} \text{ miles per second} \]
- For the faster airplane:
\[ \text{Speed in miles per second} = \frac{720 \text{ miles}}{3600 \text{ seconds}} = \frac{720}{3600} = \frac{1}{5} \text{ miles per second} \]

3. **Calculate the distance traveled in 12 seconds:**
- For the slower airplane:
\[ \text{Distance in 12 seconds} = \left(\frac{1}{6} \text{ miles per second}\right) \times 12 \text{ seconds} = \frac{12}{6} = 2 \text{ miles} \]
- For the faster airplane:
\[ \text{Distance in 12 seconds} = \left(\frac{1}{5} \text{ miles per second}\right) \times 12 \text{ seconds} = \frac{12}{5} \text{ miles} = 2.4 \text{ miles} \]

4. **Find the difference in distance traveled:**
\[ \text{Difference} = \text{Distance of faster airplane} - \text{Distance of slower airplane} = 2.4 \text{ miles} - 2 \text{ miles} = 0.4 \text{ miles} \]

### Final Answer:
The faster airplane can travel **0.4 miles** more than the slower airplane in 12 seconds.

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