Let \( A(x) \) represent the cost from Company A and \( B(x) \) represent the cost from Company B.
The equation for Company A can be expressed as:
\[ A(x) = 40 + 2x \]
where \( 40 \) is the initial fee and \( 2x \) represents the cost per mile driven.
The equation for Company B can be expressed as:
\[ B(x) = 70 + 1x \]
where \( 70 \) is the initial fee and \( x \) represents the cost per mile driven.
To find the interval of miles driven \( x \) for which Company A is cheaper than Company B, we need to set up the inequality:
\[ A(x) < B(x) \]
Substituting the equations gives:
\[ 40 + 2x < 70 + 1x \]
Now, let's solve this inequality step-by-step:
1. Subtract \( 1x \) from both sides:
\[ 40 + 2x - 1x < 70 \]
\[ 40 + x < 70 \]
2. Subtract \( 40 \) from both sides:
\[ x < 70 - 40 \]
\[ x < 30 \]
Thus, the interval of miles driven \( x \) for which Company A is cheaper than Company B is:
\[ x < 30 \]
In conclusion, Company A is cheaper than Company B when Maya drives fewer than 30 miles.