Answer
a) $2$ hours $6$ minutes
b) time is greater than $2.1$ hours
Work Step by Step
Let the cost be denoted by $y$ and the number of hours be denoted by $x$.
The total cost will be the sum of the cost of the parts and the labor cost, which is obtained by multiplying the total hours with cost per hour.
Then $$y_{dealership} = 24 + 99x.$$ Similarly, $$y_{local mechanic} = 45 + 89x.$$
a) When the cost becomes equal,
$$\begin{align}
y_{dealership} &= y_{local mechanic}\\
24 + 99x & = 45 + 89x.
\end{align}$$ Subtract $89x$ from both sides $$24 + 10x = 45.$$ Subtract $24$ from both sides $$10x = 21.$$ Divide both sides by $10$ $$x = 2.1.$$ Thus the cost becomes same at $2.1$ hours or $2$ hours $6$ minutes. ($0.1$ hours is $0.1 \times 60=6$ minutes).
b) The repairs cost less than the dealership when
$$\begin{align}
y_{dealership} &> y_{local mechanic}\\
24 + 99x & > 45 + 89x.
\end{align}$$ Subtract $89x$ from both sides $$24 + 10x > 45.$$ Subtract $24$ from both sides $$10x > 21.$$ Divide both sides by $10$ $$x > 2.1.$$ Thus the repairs cost less than the dealership after more than $2.1$ hours.
