A car travels at a constant speed of x miles per hour. Which of the following expressions gives the distance, in miles, the car will travel in t hours?

Rationale

x t gives the distance the car will travel in t hours.

When a car travels at a constant speed of x miles per hour for t hours, the distance traveled can be calculated using the formula: distance = speed × time. Therefore, multiplying speed (x) by time (t) gives the correct expression for distance.

A (x + t) YOUR ANSWER

This expression simply adds the speed and time together, which does not represent a physical distance traveled. Distance is not the sum of speed and time; instead, it is the product of these two quantities. Therefore, this option does not provide the correct relationship for calculating distance.

B (t/x) YOUR ANSWER

This expression suggests dividing time by speed, which is not a valid formula for distance. Instead, it yields a time unit (in hours per mile), which does not represent the distance traveled. To find distance, one must multiply speed by time rather than divide.

C (x t) CORRECT

This is the correct expression for distance traveled. It follows the formula distance = speed × time, where 'x' represents the speed in miles per hour and 't' represents the time in hours. Thus, multiplying these two gives the total distance in miles.

D ((x t)^2) YOUR ANSWER

This expression squares the product of speed and time, resulting in a value that represents the area rather than distance. While it maintains the units of distance squared, it does not align with the correct formula for calculating distance, which is a linear relationship rather than a quadratic one.

Conclusion

To determine the distance traveled by a car moving at a constant speed, the formula distance = speed × time is essential. In this case, the expression x t accurately captures this relationship, providing the total distance in miles. The other options fail to represent the fundamental principles of motion and distance calculation, emphasizing the importance of using the correct formula in physics problems.

A car travels at a constant speed of x miles per hour. Which of the following expressions gives the distance, in miles, the car will travel in t hours?

x t gives the distance the car will travel in t hours.

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