Sarah, a logistics manager, is evaluating the delivery times for a company van. The van travels 120 miles on a highway and 200 miles through a city zone. Its speed in the city is 10 mph slower than its highway speed ($r$). The city portion takes 2 hours longer than the highway portion. Sarah sets up the equation $\frac{120}{r} + 2 = \frac{200}{r - 10}$ to solve for $r$. Match each mathematical expression from her setup to its real-world meaning.

A logistics analyst is solving the rational equation $\frac{12}{r} + 2 = \frac{20}{r - 1}$ to determine the speed $r$ (in mph) of a delivery van on a flat route. Arrange the following algebraic steps in the correct order to solve for $r$.

A logistics coordinator at a shipping company is modeling the travel time for a delivery van. The van travels 20 miles on a challenging mountain route at an average speed of $r - 1$ miles per hour. Which algebraic expression correctly represents the time, in hours, the van spent on this mountain route?

Validating Solutions in Motion Applications

A logistics coordinator is modeling a delivery trip using the equation $\frac{12}{r} + 2 = \frac{20}{r - 1}$. In this model, the constant 2 indicates that the first segment ($\frac{12}{r}$) takes 2 hours longer than the second segment ($\frac{20}{r - 1}$).

An operations coordinator is modeling a delivery vehicle's route to optimize fuel efficiency. The route has a highway segment and a city segment. The travel time for the city segment is modeled by the algebraic expression $\frac{20}{r-15}$ hours, where 20 is the distance in miles. In this expression, the denominator $r - 15$ represents the vehicle's ____ on the city segment.

Documenting the Problem-Solving Strategy for Uniform Motion in Logistics