document.write( "Question 341688: Santiago is walking to school, which is straight down the road 500m from his home. He starts out by walking at 2m/s for 2 minutes until he gets to a stop light. He waits 30 seconds and then realizes that he has left an important essay at the front door, so he runs home at 5m/s. He had forgotten his keys, so he bangs on the door for 3 minutes until his brother Tomas answers. He grabs his essay and runs to school without stopping at 4m/s, arriving just as the warning bell rings.
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Algebra.Com's Answer #244733 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "First we will change the speeds from meters per second to meters per\r\n" );
document.write( "minute.\r\n" );
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document.write( "2 meters per second is 120 meters per minute.\r\n" );
document.write( "5 meters per second is 300 meters per minute.\r\n" );
document.write( "4 meters per second is 240 meters per minute.\r\n" );
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document.write( "Here is the graph, where x is the time in minutes, and y is the\r\n" );
document.write( "distance from home in meters.\r\n" );
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document.write( "He starts at the origin(0min,0m). His goal is to reach the green line which \r\n" );
document.write( "is 500 meters. The green line's equation is \r\n" );
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document.write( "He starts out by walking at 120 m/min for 2 minutes. \r\n" );
document.write( "So at the end of 2 minutes he has traveled 240 meters.\r\n" );
document.write( "So we draw a line from (0min,0m) to the point (2min,240m) to indicate the\r\n" );
document.write( "first part of his trip:\r\n" );
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document.write( "Now we find the equation of the line through (0,0) and (2,240) which is\r\n" );
document.write( " for the time interval  \r\n" );
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document.write( " I assume you know how to find the equation of a line\r\n" );
document.write( "through two points. \r\n" );
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document.write( "He waits at the stoplight for 30 second ( a minute), so\r\n" );
document.write( "we draw a horizontal line from (2min,240m) to (2.5min,240m), since while\r\n" );
document.write( "waiting at the stoplight he has not moved any closer to the green\r\n" );
document.write( "line.\r\n" );
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document.write( "The equation of that horizontal line is \r\n" );
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document.write( " for time interval \r\n" );
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document.write( "Next, he runs home at 5m/s or 300m/min. Now since ,\r\n" );
document.write( "and his distance back home is 240m, that takes him minutes.\r\n" );
document.write( "so we draw a line from (2.5min,240m) back to the horizontal axis .8 of a minute\r\n" );
document.write( "later which is 2.5+.8 or 3.3 minutes, to the point (3.3min,0m):\r\n" );
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document.write( "So find the equation of the line through (2.5,240) and (3.3,0) which is \r\n" );
document.write( "y=-300x+990 for the time interval \r\n" );
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document.write( "Next he waits 3 minutes at home until his brother answers. so that's\r\n" );
document.write( "a horizontal line from (3.3min,0m) to (6.3min,0m)\r\n" );
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document.write( "The equation of that line is the equation of the x-axis or \r\n" );
document.write( "y=0 for the time interval \r\n" );
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document.write( "Finally he runs the whole 500 m to school without stopping at \r\n" );
document.write( "4m/s or 240m/min. We use minutes.\r\n" );
document.write( "So we draw a line from (6.3min,0m) to (6.3min+min,500m).\r\n" );
document.write( "To add the minutes min.\r\n" );
document.write( "So we draw the line from (6.3min,0m) to (,500m).\r\n" );
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document.write( "The equation of the line through (6.3,0) and (,500) is\r\n" );
document.write( "y= 240x-1512 for the time interval .\r\n" );
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document.write( "If you don't know how to find the equation of a line through 2 points,\r\n" );
document.write( "then post again asking how.  It amounts to using the slope formula and\r\n" );
document.write( "the point-slope formula.\r\n" );
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document.write( "So, since he left home the first time, it took him minutes,\r\n" );
document.write( "or 8 minutes and 23 seconds to get to school. \r\n" );
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document.write( "Edwin

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