To determine how far a train will travel in 4.5 hours if it travels 270 miles in 3 hours, we can follow these steps:
1. Determine the speed of the train:
- The train travels 270 miles in 3 hours.
- Speed is calculated by dividing the distance traveled by the time taken. Thus, the speed of the train is:
[tex]\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{270 \text{ miles}}{3 \text{ hours}} = 90 \text{ miles per hour}
\][/tex]
2. Calculate the distance traveled in 4.5 hours:
- Now that we know the train travels at a speed of 90 miles per hour, we can determine the distance it will travel in 4.5 hours by multiplying the speed by the time:
[tex]\[
\text{Distance} = \text{Speed} \times \text{Time} = 90 \text{ miles per hour} \times 4.5 \text{ hours} = 405 \text{ miles}
\][/tex]
Thus, the train will travel 405 miles in 4.5 hours. Therefore, the correct answer is:
C) 405 miles
