Question

A plumber charges $50 for a service call plus $80 per hour. If she spends no longer than 8 hours a day at any one site, find a linear function that represents her total daily charges C (in dollars) as a function of time t (in hours) spent at any one given location.

Answer 1

`C(t)=80t+50, \text{ for }t\leq 8`.

Explanation:

Let C represent total daily charges in dollars and t represent time in hours.

We have been given that a plumber charges $50 for a service call plus $80 per hour.

The amount charged for t hours would be
`80t`.

The total amount charged for t hours would be
`C(t)=80t+50`.

We are also told that plumber spends no longer than 8 hours a day at any one site, this means that time t have a restriction as:

`t\leq 8`

Therefore, our required cost function would be
`C(t)=80t+50, \text{ for }t\leq 8`.