document.write( "Question 1156576: Hi
\n" ); document.write( "A man walks at 4/5 of his speed to his office and is late by 5 min. What is the time it takes to reach his office if he walks at 3/4 of his speed.\r
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Algebra.Com's Answer #779294 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "The original formulation in the post is  FAR  from to be  PERFECT.\r
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\n" ); document.write( "\n" ); document.write( "The  PERFECT  and  PRECISELY  CORRECT  formulation is  THIS:\r
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document.write( "    A man walks at 4/5 of his \"highlight%28REGULAR%29\"speed to his office and is late by 5 min. \r\n" );
document.write( "    What is the time it takes to reach his office if he walks at 3/4 of his \"highlight%28REGULAR%29\" speed.\r\n" );
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\n" ); document.write( "\n" ); document.write( "I will solve the problem with this formulation.\r
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document.write( "Let \"d\" be the distance to the office, and let \"u\" be the regular speed.\r\n" );
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document.write( "Then the condition produces this time equation\r\n" );
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document.write( "    \"d%2F%28%284%2F5%29%2Au%29\" - \"d%2Fu\" = 5 minutes.\r\n" );
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document.write( "Simplify\r\n" );
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document.write( "    \"%285d%29%2F%284u%29\" - \"d%2Fu\" = 5 minutes,   or\r\n" );
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document.write( "    \"d%2F%284u%29\" = 5 minutes,   or\r\n" );
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document.write( "     \"d%2Fu\" = 4*5 = 20 minutes.\r\n" );
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document.write( "So, his REGULAR time to get the office is 20 minutes.\r\n" );
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document.write( "Now, if he moves at  \"3%2F4\"  of his refular speed, it will take  \"20%2A%284%2F3%29\" = \"80%2F3\" = \"26\"\"2%2F3\" minutes = 26 minutes and 40 seconds\r\n" );
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document.write( "to get the office.     ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "Same idea can be presented in other form.\r
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document.write( "Let T be the regular time to get the office (moving at regular speed).\r\n" );
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document.write( "Then with the speed of \"4%2F5\"  of the regular, the time will be  \"%285%2F4%29T\".\r\n" );
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document.write( "Then the condition says us that\r\n" );
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document.write( "    \"%285%2F4%29T\" - T = 5 minutes,  or\r\n" );
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document.write( "    \"%281%2F4%29T\" = 5 minutes,\r\n" );
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document.write( "which means  T = 4*5 = 20 minutes (regular time).\r\n" );
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document.write( "Then with the speed of  \"3%2F4\"  of the regular, the time will be  \"20%2A%284%2F3%29\" = \"80%2F3\" = 26 minutes and 40 seconds (the same answer).\r\n" );
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