An airline flies, two different planes over the same route. The faster of the two planes travels at an average speed of 540 mile per hour,and the other plane travels at an average speed of 450 miles per hour. How many more miles can the faster plane travel in 12 seconds than the slower plane?

Options

A. `(1)/(5)`
B. `(3)/(10)`
C. `9`
D. `18`

Answer

To solve the problem, we need to calculate how far each plane travels in 12 seconds and then find the difference between the distances traveled by the faster and slower planes.

### Step-by-Step Solution:

1. **Convert the speeds from miles per hour to miles per second**:
- The faster plane travels at 540 miles per hour.
- The slower plane travels at 450 miles per hour.
- Since there are 3600 seconds in an hour, we can convert the speeds as follows:
- For the faster plane:
\[ \text{Speed in miles per second} = \frac{540 \text{ miles}}{3600 \text{ seconds}} = \frac{540}{3600} \text{ miles/second} \]
- For the slower plane:
\[ \text{Speed in miles per second} = \frac{450 \text{ miles}}{3600 \text{ seconds}} = \frac{450}{3600} \text{ miles/second} \]

2. **Calculate the distance traveled in 12 seconds**:
- For the faster plane:
\[ \text{Distance in 12 seconds} = \text{Speed} \times \text{Time} = \left(\frac{540}{3600}\right) \times 12 = \frac{540 \times 12}{3600} = \frac{6480}{3600} = \frac{54}{30} \text{ miles} \]
- For the slower plane:
\[ \text{Distance in 12 seconds} = \text{Speed} \times \text{Time} = \left(\frac{450}{3600}\right) \times 12 = \frac{450 \times 12}{3600} = \frac{5400}{3600} = \frac{45}{30} \text{ miles} \]

3. **Find the difference in distances traveled**:
- Now, we subtract the distance traveled by the slower plane from the distance traveled by the faster plane:
\[ \text{Difference} = \frac{54}{30} - \frac{45}{30} = \frac{54 - 45}{30} = \frac{9}{30} \]
- Simplifying this gives:
\[ \frac{9}{30} = \frac{3}{10} \]

4. **Conclusion**:
- The faster plane can travel \(\frac{3}{10}\) miles more than the slower plane in 12 seconds.

### Final Answer:
The faster plane can travel \(\frac{3}{10}\) miles more than the slower plane in 12 seconds.

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