Question

Joe’s Body Shop charges $25 for parts and $50 per hour to fix the brakes on a car. Kathy’s Body Shop charges $70 for parts and $40 per hour for the same type of work.

Let x represent the length of time to fix the brakes on a car.

c. When will the amount charged by Joe and Kathy be the same? Show how you determine your answer.

Answer 1

Let me just write this simply.
Joe's parts: $25 Joe's hourly rate for brakes: $50/hr
Kathy's parts:$70 Kathy's hourly rate: $40/hr
x = time (to fix the brakes)
So both will start with an initial charge for parts. Joe: $25, and Kathy: $70
Then for each hour, your price goes up...
Here is a table.
0 hrs 1 hr 2 hrs 3 hrs 4 hrs 5hrs 6 hrs
Joe 25 75 125 175 225 275 325
Kathy 70 110 150 190 230 270 310

So look at the table, notice how joe's prices always end in 5, and Kathy's always end in 0. Because neither Joe's or Kathy's rates go up by a number that ends in 5, they will never be the same.

Answer: never