Here's one more problem to try on your own. Think back to the This activity might not be viewable on your mobile device.applet you used.

Change the situation so that the boy gives the girl a 25 step head-start. He travels at 5 steps per second and she travels at 3 steps per second. Both start at their house and move toward the tree 100 steps away. Does the boy pass up the girl?  If so, when and where?

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Hint

First, you need to set up a system of equations. Let x = the number of seconds since the boy left the house. Lety= the number of steps they are from the house.

girl's distance:    y = 25 + 3x
boy's distance:    y = 5x

To solve this system using graphs, enter both equations into the calculator.

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Solution

First, you need to set up a system of equations. Let x = the number of seconds since the boy left the house. Lety = the number of steps they are from the house.

girl's distance:    y= 25 + 3x
boy's distance:    y= 5x

To solve this system using graphs, enter both equations into the calculator.

Calculator equation input screen

Next, adjust the window to fit the situation. In the APPLET, both time and distance went from 0 to 100 by 10.

Now look at the graph.

graph of intersecting lines

You can see that the boy does indeed pass the girl because there is a point of intersection. Select the CALC and intersect features of your calculator to find the coordinates of the intersection.

graph of intersecting lines with intersection points listed

The boy does pass up the girl, 62.5 steps from the house and 12.5 seconds after he started.

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