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Question

# Two walkers start walking on different paths in the town park. Walker A starts at the 0.5m mark on his path and walks at a speed of lm/sec. Walker B starts at the 2m mark on her path and walks at a speed of 0.5m/sec. a) Make a table the keeps track of where each walker is over ten seconds of time. Walker A( , ) Walker B( , ) b) Where does it appear that the two walkers meet? c) Use the starting point and speed to write an equation for each walker: Walker A:_______________________ Walker B: ___________________________ d) Graph the two equations on the same set of axes.

Solution

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a) Assuming the walkers are walking in the same direction, the positions of both walkers will increase over the ten seconds. Since Walker A is walking at a rate of 1 m/s, his position will increase by 1 m for each second. Since Walker B is walking at a rate of 0.5 m/s, her position will increase by 0.5 m for each second. The table for their positions over the first ten seconds is then:

Number of Seconds Walker A Walker B
0 0.5 2
1 1.5 2.5
2 2.5 3
3 3.5 3.5
4 4.5 4
5 5.5 4.5
6 6.5 5
7 7.5 5.5
8 8.5 6
9 9.5 6.5
10 10.5 7

b) From the table, the two walkers have the same position of 3.5 m after 3 seconds.

c) The slope-intercept form of a line is $y=mx+b$ where $m$ is the slope and $b$ is the $y$-intercept. The starting points of each walker is the $y$-intercept of their line and their speeds are the slopes. Since Walker A has a speed of $m=1$ m/s and a starting point of $b=0.5$ m, then the equation for Walker A is $y=x+0.5$. Since Walker B has a speed of $m=0.5$ m/s and a starting point of $b=2$ m, then the equation for Walker B is $y=0.5x+2$.

d) Plot the points from the table you made in part a). Then connect the points with lines. The graph of Walker A's equation is shown below in blue and the graph of Walker B's equation is shown in green:

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