A Daily Routine

Graph 12 by Andreea Cornea

Jenny is a 7th grader at Davis Drive Middle School and also a year round swimmer for YOTA (YMCA of the Triangle Area) team. She lives in walking distance from school and the Cary YMCA, where she does swim practices daily. Her house is a little closer to the Cary YMCA than it is to school. Everyday after school, she has swim practice at 3:40 pm.  At 3 pm she leaves school and walks home at a constant speed to pick up her swim bag and gear. She gets home at 3:15 pm. She leaves right away for the YMCA, walking at a faster constant speed than she did on her way home, as she is in a hurry to get there early in order to have time to dress. She gets at the YMCA at 3:25 pm. She still has 15 minutes at the YMCA to dress and get ready for practice, and to chat with her teammates. The graph represents the distance from Jenny's current position to her home during the time from the end of school at  3:00 pm to the beginning of practice at 3:40 pm.

The x-axis represents the time, in minutes, from 3 pm to 3:40 pm, with 3:00 pm being the origin and 3:40 pm being the ending. The scale on the x-axis is 1 to 5 minutes. The graph is over 8 units, that is, 40 minutes. The y-axis represents Jenny's distance from home, in miles, at any given time between 3:00 pm and 3:40 pm. The distance range is from 0 to 7 units, that is, from 0 to 0.7 miles. The scale on y-axis is 1 to 0.1 miles. The y-intercept represents the distance from school to Jenny's home which is 0.7 miles. She walked this distance in 15 minutes. During this time, Jenny's distance from home decreases at a constant rate as she walks toward home at a constant speed. The graph is a line segment with negative slope. She gets home at 3:15 pm; it is represented by the point where the graph touches the x-axis, that is, Jenny's distance from home is 0 (Jenny is at home). Then, she takes her swim gear and starts walking to the YMCA right away. She walks the 0.6 miles distance from home to the YMCA in 10 minutes. During this time, Jenny's distance from home increases at a constant rate as she walks away from home at a constant speed, but faster than before. The graph is a line segment with positive slope, steeper than the first segment (the slope of the second segment is greater than the absolute value of the slope of the first segment). At 3:25 pm she gets at the YMCA, where she stays until the start of the practice at 3:40 pm. During the last 15 minutes, Jenny's distance from home remains the same, it is constant and represents the distance from the YMCA to her house, as she stays there all that time. The graph is a horizontal line segment.

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