NAME: _____________________________________________ PERIOD: ________ DATE: __________________
And We’re Off!! It’s a Turtle Race Jose, John and Jesse decided to have a race to see which of their turtles would win. They designed a racetrack in John’s back yard that was 5 yards long and wide enough so that the turtles could be positioned beside each other. Jose’s turtle was the smallest and moved faster than the others. In 5 minutes he traveled 40 inches and 15 minutes after the start of the race he had reached the 80 inch marker. He got off to a quick start but soon became distracted by his surroundings, causing him to slow down and eventually stop to enjoy a few bites of grass during the race. Five minutes later Jose’s turtle was still at the 80 inch marker. John’s turtle was the largest and even though he moved rather slowly he never changed his pace or stopped to eat. Ten minutes after the race began he had traveled 40 inches and 10 minutes later he was at the 80 inch marker. Jesse’s turtle was neither the fastest nor slowest. Five minutes after the race began he was still sitting at the starting line with just his head poking out of his shell. He sat motionless and watched as the other two turtles move ahead of him. At 10 minutes after the race began Jesse’s turtle started to move quickly, traveling 25 inches in 5 minutes. Jesse began cheering excitedly for his turtle and became hopeful that he might win the race! Fifteen minutes from the start of the race Jesse watched the unthinkable happen; within the next five minutes his turtle returned to the starting line and withdrew inside his shell. After 30 minutes of turtle racing the boys decided to end the race because Jeremy and James came by and invited them to a game of soccer. By then, Jose’s turtle was still at the 80-‐inch marker eating grass, John’s turtle was at the 120-‐inch marker and Jesse’s turtle was back at the starting line. On a sheet of graph paper, sketch each turtle’s path based on the information given indicating the position vs. time. Be sure to include the following information in your graph: Monday: a. Identify the independent and dependent variables. b. Use reasonable units and scales for both variables. c. Distinguish graphically each turtle’s movement. Indicate the amount of time the race was run and the distance to the finish line on the graph. Tuesday: d. Is the graph discrete or continuous? Justify your answer. e. Label all parts of the graph including each interval. f. Determine the domain and range of each interval. Thursday: g. Determine if each turtle’s graph represents a function. h. Determine the type of correlation for each interval. i. Does each interval have a constant rate of change? What is the slope for each interval. j. Create a 3CPC for each interval. Friday: k. Determine the equation for each interval, use your 3CPCs and explain graphically. l. Did any turtle reach the marker that indicated “¼ distance remaining” to the finish line? When the race ended, how far from the finish line was each turtle? If the race had continued who would have won the race? How much time would this turtle have needed to win.