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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. $\newline$ What is the domain of $D(t)$ ? $\newline$ Choices: $\newline$ (A)all real numbers from $0$ to $80$ $\newline$ (B)all whole numbers from $0$ to $3$ $\newline$ (C)all real numbers from $0$ to $3$ $\newline$ (D)all whole numbers from $0$ to $80$

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Domain and range of linear functions: word problems

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Q. 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.

\newline

What is the domain of

D(t)

?

\newline

Choices:

\newline

(A)all real numbers from

0

to

80

\newline

(B)all whole numbers from

0

to

3

\newline

(C)all real numbers from

0

to

3

\newline

(D)all whole numbers from

0

to

80

Determine Domain of Function: We need to determine the domain of the function $D(t)$ , which represents the distance traveled by the train after $t$ hours at cruising speed. $\newline$ The train travels at a constant speed of $80$ miles per hour.
Calculate Time to Travel: To find the domain, we need to consider the time it takes for the train to travel $240$ miles at $80$ miles per hour. $\newline$ We calculate the time by dividing the distance by the speed: $t = \frac{240 \text{ miles}}{80 \text{ miles per hour}}$ .
Find Domain of $D(t)$ : Performing the calculation gives us $t = 3$ hours. $\newline$ This means that the train will take $3$ hours to travel the $240$ miles at cruising speed.
Find Domain of D(t): Performing the calculation gives us $t = 3$ hours. $\newline$ This means that the train will take $3$ hours to travel the $240$ miles at cruising speed.The domain of $D(t)$ is the set of all possible values of $t$ , which is the time in hours that the train travels at cruising speed. $\newline$ Since the train can travel for any fraction of time up to $3$ hours, the domain includes all real numbers from $0$ to $3$ .

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