document.write( "Question 173044: Please help me solve this equation:\r
\n" ); document.write( "\n" ); document.write( "You commute 56 miles one way to work. The trip to work takes 10 minutes longer than the trip to home. Your average speed on the trip home is 8 miles per hour faster. What is your average speed on the trip home?\r
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Algebra.Com's Answer #127895 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
Note: 10 minutes = 1/6 of an hour\r
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\n" ); document.write( "\n" ); document.write( "Since the distance of the commute is 56 miles, this means that \"d=56\"\r
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\n" ); document.write( "\n" ); document.write( "Going to Work:\r
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\n" ); document.write( "\n" ); document.write( "Since \"The trip to work takes 10 minutes longer than the trip to home\", this means that the time is \"t%2B10\" (in minutes) or \"t%2B1%2F6\" (in hours)\r
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\n" ); document.write( "\n" ); document.write( "We'll use the expression \"t%2B1%2F6\"\r
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\n" ); document.write( "\n" ); document.write( "\"d=rt\" Start with the distance rate time formula\r
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\n" ); document.write( "\n" ); document.write( "\"56=r%28t%2B1%2F6%29\" Plug in \"d=56\" and replace \"t\" with \"t%2B1%2F6\" \r
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\n" ); document.write( "\n" ); document.write( "\"56=r%28%286t%2B1%29%2F6%29\" Combine \"t\" and \"1%2F6\" to get \"%286t%2B1%29%2F6\"\r
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\n" ); document.write( "\n" ); document.write( "\"56%2F%28%286t%2B1%29%2F6%29=r\" Divide both sides by \"%286t%2B1%29%2F6\" to isolate \"r\"\r
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\n" ); document.write( "\n" ); document.write( "\"56%286%2F%286t%2B1%29%29=r\" Multiply 56 by the reciprocal of \"%286t%2B1%29%2F6\".\r
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\n" ); document.write( "\n" ); document.write( "\"336%2F%286t%2B1%29=r\" Multiply 56 and 6 to get 336\r
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\n" ); document.write( "\n" ); document.write( "So after isolating \"r\", we get \"r=336%2F%286t%2B1%29\"\r
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\n" ); document.write( "\n" ); document.write( "Coming Home:\r
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\n" ); document.write( "\n" ); document.write( "Now because the \"average speed on the trip home is 8 miles per hour faster\", this means that the new rate is \"r%2B8\"\r
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\n" ); document.write( "\n" ); document.write( "\"d=rt\" Go back to the distance rate time formula\r
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\n" ); document.write( "\n" ); document.write( "\"56=%28r%2B8%29t\" Plug in \"d=56\" (the commute distance hasn't changed) and replace \"r\" with \"r%2B8\" (since the speed is 8 mph greater)\r
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\n" ); document.write( "\n" ); document.write( "\"56=%28336%2F%286t%2B1%29%2B8%29t\" Plug in \"r=336%2F%286t%2B1%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"56=%28336%2F%286t%2B1%29%29t%2B8t\" Distribute\r
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\n" ); document.write( "\n" ); document.write( "\"56%286t%2B1%29=336t%2B8t%286t%2B1%29\" Multiply EVERY term by the LCD \"6t%2B1\" to clear the fractions.\r
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\n" ); document.write( "\n" ); document.write( "\"336t%2B56=336t%2B48t%5E2%2B8t\" Distribute\r
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\n" ); document.write( "\n" ); document.write( "\"0=336t%2B48t%5E2%2B8t-336t-56\" Subtract 336t from both sides. Subtract 56 from both sides.\r
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\n" ); document.write( "\n" ); document.write( "\"0=48t%5E2%2B8t-56\" Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "Notice we have a quadratic equation in the form of \"at%5E2%2Bbt%2Bc\" where \"a=48\", \"b=8\", and \"c=-56\"\r
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\n" ); document.write( "\n" ); document.write( "Let's use the quadratic formula to solve for t\r
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\n" ); document.write( "\n" ); document.write( "\"t+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29\" Start with the quadratic formula\r
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\n" ); document.write( "\n" ); document.write( "\"t+=+%28-%288%29+%2B-+sqrt%28+%288%29%5E2-4%2848%29%28-56%29+%29%29%2F%282%2848%29%29\" Plug in \"a=48\", \"b=8\", and \"c=-56\"\r
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\n" ); document.write( "\n" ); document.write( "\"t+=+%28-8+%2B-+sqrt%28+64-4%2848%29%28-56%29+%29%29%2F%282%2848%29%29\" Square \"8\" to get \"64\". \r
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\n" ); document.write( "\n" ); document.write( "\"t+=+%28-8+%2B-+sqrt%28+64--10752+%29%29%2F%282%2848%29%29\" Multiply \"4%2848%29%28-56%29\" to get \"-10752\"\r
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\n" ); document.write( "\n" ); document.write( "\"t+=+%28-8+%2B-+sqrt%28+64%2B10752+%29%29%2F%282%2848%29%29\" Rewrite \"sqrt%2864--10752%29\" as \"sqrt%2864%2B10752%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"t+=+%28-8+%2B-+sqrt%28+10816+%29%29%2F%282%2848%29%29\" Add \"64\" to \"10752\" to get \"10816\"\r
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\n" ); document.write( "\n" ); document.write( "\"t+=+%28-8+%2B-+sqrt%28+10816+%29%29%2F%2896%29\" Multiply \"2\" and \"48\" to get \"96\". \r
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\n" ); document.write( "\n" ); document.write( "\"t+=+%28-8+%2B-+104%29%2F%2896%29\" Take the square root of \"10816\" to get \"104\". \r
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\n" ); document.write( "\n" ); document.write( "\"t+=+%28-8+%2B+104%29%2F%2896%29\" or \"t+=+%28-8+-+104%29%2F%2896%29\" Break up the expression. \r
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\n" ); document.write( "\n" ); document.write( "\"t+=+%2896%29%2F%2896%29\" or \"t+=++%28-112%29%2F%2896%29\" Combine like terms. \r
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\n" ); document.write( "\n" ); document.write( "\"t+=+1\" or \"t+=+-7%2F6\" Simplify. \r
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\n" ); document.write( "\n" ); document.write( "So the possible time values (coming home) are \"t+=+1\" or \"t+=+-7%2F6\" \r
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\n" ); document.write( "\n" ); document.write( "However a negative time does NOT make sense. So the only answer is \"t+=+1\"\r
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\n" ); document.write( "\n" ); document.write( "So the time to commute home is 1 hour. \r
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\n" ); document.write( "\n" ); document.write( "Note: This means that the time to get to work is 1 hour and 10 minutes (or 70 minutes)\r
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\n" ); document.write( "\n" ); document.write( "\"d=rt\" Go back to the distance rate time formula\r
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\n" ); document.write( "\n" ); document.write( "\"56=r%281%29\" Plug in \"d=56\" and \"t=1\" (which is the time coming home)
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\n" ); document.write( "\n" ); document.write( "\"56=r\" Multiply\r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So the solution is \"r=56\" \r
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\n" ); document.write( "\n" ); document.write( "This means that the average speed coming home is 56 miles per hour.
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