14. Two cars leave town at the same time traveling in opposite directions. One travels \( 51 \mathrm{mi} / \mathrm{h} \) and the other travels \( 45 \mathrm{mi} / \mathrm{h} \). In how many hours will they be 432 miles apart?

To find out how many hours it will take for the two cars to be 432 miles apart, we can first add their speeds together because they are moving in opposite directions. So, \( 51 \text{ mi/h} + 45 \text{ mi/h} = 96 \text{ mi/h} \). Next, to find the time (\( t \)) it takes for them to be 432 miles apart, we use the formula: \[ \text{Distance} = \text{Speed} \times \text{Time} \] Rearranging this for time gives us: \[ t = \frac{\text{Distance}}{\text{Speed}} = \frac{432 \text{ miles}}{96 \text{ mi/h}} = 4.5 \text{ hours} \] Thus, it will take 4.5 hours for the two cars to be 432 miles apart.