Question

A car 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?

Answer 1

For the same amount set up two equations set equal to each other.
$70h + 130 = 80h + $40
Subtract 80h from both sides
-10h + 130 = 40
subtract 130 from both sides
-10h = -90 divide both sides by -10
h = 9 hours

CHECK
70(9) + 130 = $760
80(9) + 40 = $760

Answer 2

9 hours

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