As a supply chain analyst for a marine transport company, you are using the distance, rate, and time strategy to evaluate the uniform motion speeds of a delivery barge. The barge completes a standard round trip, traveling upstream to a manufacturing plant and then returning downstream to the original port. When translating your rate and time data into an algebraic equation, which fundamental relationship must you recall to successfully solve the problem?

In uniform motion problems involving a boat traveling between two fixed points, the distance calculated for the upstream trip must be equal to the distance calculated for the downstream trip if the boat starts and ends at the same dock.

A logistics coordinator at a marine transport firm is documenting the standard procedure for calculating the uniform motion speeds of delivery barges. When a barge travels to a destination upstream and returns downstream to the same dock, the coordinator must follow a specific algebraic strategy to find the unknown speeds. Arrange the following steps of this problem-solving process in the correct order.

As a logistics coordinator for a river taxi service, you are reviewing the 'distance, rate, and time' strategy used to calculate vessel speeds for round trips. Match each mathematical component of the strategy with its primary purpose in the problem-solving process.

Variable Representation in Marine Logistics

A logistics analyst for a river transport company is modeling a cargo vessel's shipping route. Due to the river's current, the vessel's downstream speed is 4 miles per hour faster than its upstream speed. If the analyst represents the vessel's upstream speed in miles per hour with the variable $r$, what algebraic expression represents the downstream speed in miles per hour?

____ (Note: Express your answer in terms of $r$ without units or spaces, e.g., $r+2$)

Guiding a Trainee in Route Speed Modeling