document.write( "Question 79616: not in book Help!!\r
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Algebra.Com's Answer #57139 by Edwin McCravy(20056) $\"\"$ $\"About$
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document.write( "Mandy begins bicycling west at 30 miles per hour at 11 am. If Liz leaves from\r\n" );
document.write( "the same point 20 minute latera bicycling west at 36 miles per hour, when will\r\n" );
document.write( "she catch Mandy?\r\n" );
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document.write( "First I'll show you how to do it in your head. Then I'll show you how\r\n" );
document.write( "your teacher wants you to work it.\r\n" );
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document.write( "20 minutes is 1/3 of an hour, so since Mandy can go 30 miles in one hour,\r\n" );
document.write( "she goes 10 miles in that 1/3 of an hour. So she's ahead of Liz by 10 miles\r\n" );
document.write( "when Liz starts out.  Liz goes 6 mph faster than Mandy, so she can make\r\n" );
document.write( "up 6 miles of Mandy's 10 mile lead in one hour.  She can make up 2 more\r\n" );
document.write( "miles of Mandy's lead in 1/3 of an hour, and the remaining 2 miles of Mandy's\r\n" );
document.write( "lead in another 1/3 of an hour. So it will take her 1 2/3 hours or an hour\r\n" );
document.write( "and 40 minutes.  Since Liz started at 11:20, she will catch Mandy at 1 PM.\r\n" );
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document.write( "But your teacher will not accept that way, but it is interesting that you\r\n" );
document.write( "can do it in your head.  But you might mention this to your teacher. Here's\r\n" );
document.write( "how your teacher wants you to do it:\r\n" );
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document.write( "Let t = the number of hours after 11 AM that Liz \r\n" );
document.write( "catches Mandy\r\n" );
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document.write( "Make this chart\r\n" );
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document.write( "         DISTANCE     RATE    TIME\r\n" );
document.write( "Liz                                \r\n" );
document.write( "Mandy                                \r\n" );
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document.write( "Mandy travels the entire time, so her time is t,\r\n" );
document.write( "Fill that in:\r\n" );
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document.write( "         DISTANCE     RATE    TIME\r\n" );
document.write( "Liz                             \r\n" );
document.write( "Mandy                           t      \r\n" );
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document.write( "Fill in their rates as 36 and 30 mph\r\n" );
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document.write( "         DISTANCE     RATE    TIME\r\n" );
document.write( "Liz                    36       \r\n" );
document.write( "Mandy                  30       t     \r\n" );
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document.write( "Liz's time is 20 minutes less than Mandy's\r\n" );
document.write( "time.  Since 20 minutes is 1/3 of an hour,\r\n" );
document.write( "Liz's time is t-1/3, so fill that in as\r\n" );
document.write( "Liz's time:\r\n" );
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document.write( "         DISTANCE     RATE    TIME\r\n" );
document.write( "Liz                    36     t-1/3\r\n" );
document.write( "Mandy                  30       t\r\n" );
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document.write( "Now use DISTANCE = RATE×TIME to fill in\r\n" );
document.write( "the two distances:\r\n" );
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document.write( "         DISTANCE     RATE    TIME\r\n" );
document.write( "Liz      36(t-1/3)     36     t-1/3\r\n" );
document.write( "Mandy       30t        30       t\r\n" );
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document.write( "Now that the chart is filled in we make\r\n" );
document.write( "our equation by noting that when Liz\r\n" );
document.write( "catches Mandy they will have traveled\r\n" );
document.write( "the SAME distance, so set their two\r\n" );
document.write( "distances equal:\r\n" );
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document.write( "     36(t - 1/3) = 30t\r\n" );
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document.write( "        36t - 12 = 30t \r\n" );
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document.write( "              6t = 12\r\n" );
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document.write( "               t = 2\r\n" );
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document.write( "2 hours past 11AM is 1PM.  So Liz catches\r\n" );
document.write( "Mandy at 1PM.\r\n" );
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document.write( "Edwin
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