Solve the problem.The line graph represents the gallons of water in a swimming pool after x hours. There is a pump that can either add or remove water from the pool. Find the slope of each line segment, and interpret each slope as a rate of change. Describe what happens to the amount of water in the pool.
A. Initially the pool contains 100 gallons of water. The pump adds water at a rate of 300 gallons per hour for one hour until there are 400 gallons of water in the pool. For the next hour the pump removes water at a rate of 50 gallons per hour. Then the pump adds water at a rate of 150 gallons per hour for two hours. Finally, the pump removes water at a rate of 150 gallons per hour for 2 hours, at which time the pool is empty.
B. Initially the pool contains 1000 gallons of water. The pump removes water at a rate of 150 gallons per hour for two hours until there are 400 gallons of water in the pool. For the next hour the pump adds water at a rate of 100 gallons per hour. Then the pump removes water at a rate of 100 gallons per hour for two hours. Finally, the pump adds water at a rate of 250 gallons per hour for 2 hours, at which time the pool contains 900 gallons of water.
C. Initially the pool contains 100 gallons of water. The pump adds water at a rate of 150 gallons per hour for two hours until there are 400 gallons of water in the pool. For the next hour the pump removes water at a rate of 100 gallons per hour. Then the pump adds water at a rate of 100 gallons per hour for two hours. Finally, the pump removes water at a rate of 250 gallons per hour for 2 hours, at which time the pool is empty.
D. Initially the pool contains 200 gallons of water. The pump adds water at a rate of 150 gallons per hour for two hours until there are 400 gallons of water in the pool. For the next hour the pump neither adds nor removes water. Then the pump adds water at a rate of 100 gallons per hour for one hour. Finally, the pump removes water at a rate of 250 gallons per hour for 3 hours, at which time the pool is empty.
Answer: C
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