Topic 19: Formulating and solving systems 145 LESSON 4: HOMEWORK Notes or additional instructions based on whole-class discussion of homework assignment: Part I. Two swimming pools are draining at constant rates. The draining of the pools begins at the same time. The above-ground pool is 72 inches deep, and is draining so that the water depth decreases at 4 inches per hour. The in-ground pool is 92 inches deep; but is being pumped out so the water depth is decreasing at 8 inches per hour. Does the water in the two pools ever have the same depth at the same point in time? If so, when does this happen, and what is the depth? 1. To answer these questions, start by completing these statements and tables The above-ground pool has a depth The in-ground pool has a depth of inches and is draining at a of inches and is draining at a rate of Inches per hour. rate of inches per hour. Time (hours) Depth (inches) Time (hours) Depth (inches) 172 0 92 Using the variables d for the depth in inches and t for the time in hours, write a rule for each pool. a. Above-ground pool: b. In-ground pool: 3. When do the two pools have the same depth? What is the depth when this happens? 4. When does each pool become empty? Copyright @ Charles A. Dana Center at the University of Texas at Austin, Learning Sciences Research Institute at the University of Illinois at Chicago, Agile Mind, Inc