Question

A1 Plumbing Service charges $35 per hour plus a $25 travel charge for a service call. Good Guys Plumbing Repair charges $40 per hour for a service call with no travel charge. How long must a service call be for the two companies to charge the same amount?

Answer 1

5 hours

Explanation:

Both total rates can be expressed as a linear function, or simple equation, with the hourly rate as the slope and fixed fee as an offset.

Converting the word problem into an algebraic equation we will use ‘h’ as the number of hours. We want to find the value of ‘h’ that will make each of the rate equations equal to each other. For A1 Plumbing the cost for service is:

`c = 35*h + 25`

For Good Guys it is:

`c = 40*h`

for both ‘c’s to be equal, the equations must equal each other:

`35*h + 25 = 40*h` we can now solve this algebraically:
`25 = 40*h – 35*h ; 25 = 5*h ; **h = 5 hours**`

CHECK:
`c1 = 35*5 + 25 = 175 + 5 = 200`
`c2 = 40*5 = 200` correct!