Math 1: Algebra, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
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Overtaking – Slope in Distance Time Graphs – Guided Notes – Section 4.04 Recall that in a distance-­‐time graph, slope represents _________________________. Example 1: In the graph below, the dashed line represents Michelle’s car and the solid line represents Sarah’s car. 8
7
6
Distance
in)Miles
5
4
3
2
1
5
–1
10
Time)in)Minutes
15
a. Find Michelle’s speed in miles per minute. b. Find Sarah’s speed in miles per minute. c. Write an equation for Michelle’s graph. d. Write an equation for Sarah’s graph. e. Write and solve an equation for the time when Michelle overtakes Sarah. 1 Math 1: Algebra, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
Date:
Example 2: The graph below shows Tony and Sasha biking to the lake, which is 8 miles from school. a. Find Tony’s speed in miles per hour. b. Find Sasha’s speed in miles per hour. c. Write equations for Tony’s line and Sasha’s lines. Tony: Sasha: d. Write and solve an equation for the time when Sasha overtakes Tony. e. When does Tony get to the lake? f. When does Sasha get to the lake? 2 Math 1: Algebra, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
Date:
Practice 1: Demetri and Yakov run around a track. The figure below shows their distance-­‐time graphs. a. Who is running faster? b. At what time does Yakov overtake Demitri? c. At what distance does Yakov overtake Demitri? d. What are both runners’ speeds? Yakov: Demitri: e. Write an equation for Yakov’s graph. f. Write an equation for Demitri’s graph. g. Write an equation with a solution that is the time at which Yakov overtakes Demitri. h. Solve the equation that you wrote in part g. Show your work and write your answer as a complete sentence. 3