Acar needs fixing and abe can fix it for $70 per hour with a $130 part, but gabe can fix it for $80 an hour with a $40 part. how long will it take for both abe and gabe to cost the same amount?

9 hours

Step-by-step explanation:

Let for x hours the amount charged by Abe and Gabe is same.

Given,

In fixing by Abe,

Fixed cost  = $ 130,

Additional cost per hour = $ 70,

So, the total charge for x hours = 130 + 70x

In fixing by Gabe,

Fixed cost = $ 40,

Additional cost per hour = $ 80,

So, the total charge for x hours = 40 + 80x

For same charge,

130 + 70x = 40 + 80x

70x = 40 + 80x - 130

70x - 80x = -90

-10x = -90

⇒ x = 9

Hence, it will take 9 hours for both Abe and Gabe to cost the same amount

answer: yes, since the line has a steeper rate of change than the exponential the y-values will be greater and they will only intersect one time.