Final answer:
The total time (T) for a round trip to a vacation resort 530 miles away when the return velocity is 5 mph slower than the outgoing velocity (x) is expressed as T(x) = 530 / x + 530 / (x - 5).
Step-by-step explanation:
To calculate the total time required for a road trip to and from a vacation resort 530 miles away, we need to create an equation based on the average velocity on the outgoing trip (x) and factor in that the average velocity on the return trip is 5 mph slower than on the outgoing trip.
Let's denote the average velocity on the outgoing trip as x miles per hour (mph). The time taken for the outgoing trip can be calculated using the formula time = distance / velocity, which is time = 530 / x.
For the return trip, the average velocity is x - 5 mph. Accordingly, the time for the return trip is 530 / (x - 5).
To express the total time (T) for both trips as a function of the outgoing average velocity (x), we add the two time expressions together:
T(x) = 530 / x + 530 / (x - 5)
This function gives us the total time required for the round trip as a function of the average velocity on the outgoing trip.