A campus maintenance technician completes an inspection in two segments. First, they use a motorized scooter for 1.5 hours at a speed of $r$ mph. Then, they switch to a utility cart for 2.25 hours, traveling at a speed 1.6 times faster than the scooter. The total distance covered is 51 miles. Match each description of the trip to its corresponding mathematical expression or equation.

A logistics coordinator is training a new hire on how to calculate average speeds for multi-segment delivery routes where the total distance and segment times are known. Arrange the following steps of the problem-solving strategy in the correct order.

A logistics fleet manager is calculating the travel parameters for a delivery drone on a two-part route. During the first segment, the drone travels for 1.5 hours at a base speed of $r$ miles per hour. During the second segment, it travels for 2.25 hours at a speed 1.6 times the base speed. Which expression correctly represents the drone's rate (speed) during the second segment?

A field service technician travels to two different job sites in one morning. During the first segment of the trip, they travel for 1.5 hours at a base rate of $r$ miles per hour. During the second segment, they travel for 2.25 hours at a rate of ${}1.6r$. If the total distance covered is 51 miles, the relationship is modeled by the equation ${}1.5r + 3.6r = 51$. In this equation, the term ${}3.6r$ represents the ____ traveled during the second segment.

A fleet management system is being programmed to calculate unknown delivery speeds for a route with a total distance of 51 miles. To correctly model the trip, the system should be programmed to set the sum of the times spent in each segment equal to the total distance of 51 miles.