To determine which of the provided equations correctly represents the distance [tex]\(d\)[/tex] in miles that a truck driver has driven as a function of time in hours [tex]\(h\)[/tex], we can analyze the relationship between distance, rate, and time.
1. Speed and Distance Relationship:
The formula that connects distance ([tex]\(d\)[/tex]), speed ([tex]\(r\)[/tex]), and time ([tex]\(t\)[/tex]) is:
[tex]\[
d = r \times t
\][/tex]
2. Given Values:
- The constant rate ([tex]\(r\)[/tex]) at which the truck driver drives is [tex]\(60\)[/tex] miles per hour.
- The time ([tex]\(t\)[/tex]) in this context is given as hours ([tex]\(h\)[/tex]).
3. Substituting the Known Values:
Using the given rate of [tex]\(60\)[/tex] miles per hour, we can substitute [tex]\(r\)[/tex] with [tex]\(60\)[/tex] and [tex]\(t\)[/tex] with [tex]\(h\)[/tex] in the formula:
[tex]\[
d = 60 \times h
\][/tex]
4. Verifying the Correct Equation:
Let's now match this derived equation with the given options:
- [tex]\(h = 60d\)[/tex]: This implies time is a function of distance and would mean [tex]\(h = \frac{d}{60}\)[/tex], which does not match our derived formula.
- [tex]\(d = 60h\)[/tex]: This matches exactly with our derived formula [tex]\(d = 60 \times h\)[/tex].
- [tex]\(h = 60 + d\)[/tex]: This implies the relationship is based on addition rather than multiplication.
- [tex]\(d = 60 - h\)[/tex]: This implies a subtractive relationship, which is incorrect in the context of a constant speed.
Therefore, the correct equation that represents the distance [tex]\(d\)[/tex] in miles the truck driver has driven as a function of time in hours [tex]\(h\)[/tex] is:
[tex]\[
d = 60h
\][/tex]
Hence, the correct choice is:
[tex]\[
d = 60h
\][/tex]
