Consider each of the following pairs of problems. What is the relationship between each pair?

**Problem 1:**

- a) Zandra travels 630 miles to Austin driving an average of 70 miles per hour. How fast would Zandra have to drive to complete a 720 mile trip in the same amount of time? How fast would Zandra have to drive to complete a 450 mile trip in the same amount of time? Is the relationship between distance and speed the same across these three examples? If so, describe the general relationship.

b) Julie makes regular trips from point A to point B. If she travels at an average speed to 60 miles per hour, it takes her 20 hours. If Julie travels at an average speed of 80 miles per hour, how long will it take? If Julie travels at an average speed of 150 miles per hour, how long will it take? It the relationship between speed and time the same across these three examples? If so, describe the general relationship.

**Problem 2:**

- a) Joe the farmer drained his grain silo into a holding bin. The silo was full and held 300 cubic meters of grain. It drained at a rate of 5 cubic meters per hour. How fast would Joe have to drain a silo that held 420 cubic meters of grain so that it took the same amount of time? How fast would Joe have to drain a silo that held 210 cubic meters of grain so that it took the same amount of time? Is the relationship between volume and rate the same across these three examples? If so, describe the general relationship.

b) Grain elevators are large containers used to fill train cars with grain that farmers have harvested. If the elevator dispenses grain at 500 cubic feet per minute, it takes 12 minutes to fill a train car. If the elevator dispenses grain at 200 cubic feet per minute, how long will it take? If the grain elevator dispenses grain at 250 cubic feet per minute, how long will it take? Is the relationship between rate and time the same across these three examples? If so, describe the general relationship.

**Problem 3:**

- Create a visual representation that demonstrates the differences between direct and inverse proportion. Explain what it shows.

Extension

Write your own problem that illustrates the difference between direct proportions and inverse proportions.