Question

#6. a lawn service charges a $6 travel fee plus $7 per hour. a competitor charges no travel fee but charges $9 per hour. after how many hours h will the two services cost the same? write and solve the equation by graphing.

Explanation:

Step1: Define cost equations

Let $C_1$ = cost of first service, $C_2$ = cost of competitor.
$C_1 = 7h + 6$
$C_2 = 9h$

Step2: Set costs equal

Find $h$ where $7h + 6 = 9h$

Step3: Solve for h

Subtract $7h$ from both sides:
$6 = 2h$
$\frac{6}{2} = h$
$h = 3$

Step4: Verify via graph

For $h=3$:
$C_1 = 7(3)+6=27$, $C_2=9(3)=27$. The lines intersect at $(3,27)$.

Answer:

After 3 hours, the two services cost the same.