Question
The amount Troy charges $30
to mow a lawn is proportional to the time it takes him to mow the lawn. Troy charges
to mow a lawn that took him 1.5
hours to mow.
Which equation models the amount in dollars,
, Troy charges when it takes him h hours to mow a lawn?
Answers
GPT-4o mini
Since the amount Troy charges is proportional to the time it takes him to mow a lawn, we can express this relationship with the equation:
\[
C = k \cdot h
\]
where \( C \) is the cost in dollars, \( h \) is the time in hours, and \( k \) is the constant of proportionality.
From the information given, Troy charges $30 for mowing a lawn, which we can consider as the amount for mowing a lawn that takes 1 hour (this assumption is valid since we do not have this information). So, if we assume he takes 1 hour to mow, then \( C = 30 \) and \( h = 1 \).
Plugging these values into the equation helps us find \( k \):
\[
30 = k \cdot 1
\]
\[
k = 30
\]
Now, we can substitute \( k \) back into our equation:
\[
C = 30h
\]
Thus, the equation that models the amount in dollars Troy charges when it takes him \( h \) hours to mow a lawn is:
\[
C = 30h
\]
\[
C = k \cdot h
\]
where \( C \) is the cost in dollars, \( h \) is the time in hours, and \( k \) is the constant of proportionality.
From the information given, Troy charges $30 for mowing a lawn, which we can consider as the amount for mowing a lawn that takes 1 hour (this assumption is valid since we do not have this information). So, if we assume he takes 1 hour to mow, then \( C = 30 \) and \( h = 1 \).
Plugging these values into the equation helps us find \( k \):
\[
30 = k \cdot 1
\]
\[
k = 30
\]
Now, we can substitute \( k \) back into our equation:
\[
C = 30h
\]
Thus, the equation that models the amount in dollars Troy charges when it takes him \( h \) hours to mow a lawn is:
\[
C = 30h
\]