1. 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?
Answer: C
The expression that gives the distance traveled by the car in t hours is x t.
The distance traveled by a car can be calculated using the formula distance = speed × time. Therefore, if the car travels at a constant speed of x miles per hour for t hours, the distance traveled is given by the expression x t.
A) x + t
This option is incorrect because it suggests that the distance is the sum of speed and time, which does not align with the standard formula for distance. Distance cannot be calculated by simply adding speed and time together.
B) t/x
This option is incorrect as it indicates the time taken to travel a distance at speed x, rather than the distance itself. The formula for distance requires multiplication of speed and time, not division.
C) x t
This option is correct because it directly follows the formula for calculating distance. By multiplying the speed (x) by the time (t), we obtain the total distance traveled by the car in miles.
D) (x t)^2
This option is incorrect as it represents the square of the distance formula, which does not apply in this context. The distance traveled should not be squared, as that would misrepresent the relationship between speed, time, and distance.
Conclusion
The expression x t correctly represents the distance traveled by the car in t hours at a constant speed of x miles per hour, aligning with the fundamental distance formula. All other options either misapply mathematical operations or misinterpret the relationship between speed and time.