Ethan’s Plumbing and Mark’s Plumbing have different ways of charging their customers. The function defined by J(t)=45t represents the total amount in dollars that Joe’s Plumbing charges for t hours of work. Mark’s Plumbing charges $40 per hour plus a $25 trip charge.

a. Which plumbing service company has a higher rate per hour? Justify your answer.

b. What domain values for both functions are reasonable in this context? Justify your answer.

c. Leyla needs to hire a plumber to fix a few things around her house. She will need plumbing service for a total of 3 hours. Which plumbing service should she go with to save money? How much will she save? Justify your answer.