8. 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 hours?
Answer: C
The distance the car will travel in hours is represented by the expression xt.
The expression that correctly gives the distance traveled by the car in hours is xt, where x is the speed in miles per hour and t is the time in hours.
A) x+t
This option incorrectly combines speed and time as a simple sum, which does not accurately represent distance. Distance is calculated by multiplying speed by time, not adding them together.
B) t+x
Similar to option A, this choice also represents a sum of time and speed, which does not provide the correct calculation for distance. The relationship between distance, speed, and time requires multiplication, making this option incorrect.
C) xt
This option accurately reflects the formula for distance, where distance is calculated by multiplying the speed (x) by the time (t) the car travels. Thus, this expression is correct.
D) (xt)²
This choice incorrectly squares the product of speed and time, which does not correspond to the definition of distance. The correct relationship between distance, speed, and time is linear, not quadratic, making this option incorrect.
Conclusion
The correct answer, xt, is the only option that appropriately describes the relationship between speed, time, and distance, following the formula Distance = Speed × Time. All other options fail to represent this fundamental concept, either by misapplying arithmetic operations or by misunderstanding the relationship between the variables involved.