Question

mabel takes an express train to visit her grandparents each summer. once the train reaches its cruising speed, it travels at a constant 80 miles per hour for 240 miles before it begins to slow down. the function d(t) represents the distance traveled by the train, in miles, after t hours at cruising speed.
what is the domain of d(t)?
all whole numbers from 0 to 80
all whole numbers from 0 to 3
all real numbers from 0 to 80
all real numbers from 0 to 3

Explanation:

Step1: Calculate total cruising time

Use $\text{time} = \frac{\text{distance}}{\text{speed}}$, so $t = \frac{240}{80} = 3$ hours.

Step2: Define domain bounds

Time $t$ starts at 0, ends at 3. Time is a continuous quantity, so $t$ can be any real number between 0 and 3 (inclusive).

Answer:

all real numbers from 0 to 3