document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=162377>Question 162377</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0618317821/algebrahomeworkh>Algebra and Trigonometry</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> please help me solve this word problem:\r<BR>\n" );
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document.write( "     On the first past of a 317-mile trip, a salesperson averaged 58 miles per hour. he averaged only 52 miles per hour on the last part of the trip because of an increased volume of traffic. the total time of the trip was 5 hours and 45 minutes. Find the amount of time at each of the two speed. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #119673 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=119673\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = amount of time spent doing 58 miles per hour.<BR>\n" );
document.write( "let y = amount of time spent doing 52 miles per hour.<BR>\n" );
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document.write( "amount of time spent doing 58 miles an hour plus amount of time spent doing 52 miles per hour equals total number of miles.<BR>\n" );
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document.write( "58*x + 52*y = 317<BR>\n" );
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document.write( "total time spent is 5 hours 45 minutes which is the same as 5.75 hours since 45 minutes is 3/4 times 60 minutes = 3/4th of an hour = .75 of an hour.<BR>\n" );
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document.write( "time spent doing 58 miles per hour plus time spent doing 52 miles an hour equals total time spent.<BR>\n" );
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document.write( "x + y = 5.75<BR>\n" );
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document.write( "you have 2 equations in 2 unknowns.<BR>\n" );
document.write( "they are:<BR>\n" );
document.write( "58*x + 52*y = 317<BR>\n" );
document.write( "x + y = 5.75<BR>\n" );
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document.write( "you can make x = 5.75 - y and substitute in other equation, or<BR>\n" );
document.write( "you can solve these simultaneously by multiplying equation 2 by 58 and then subtracting one of the equations from the other one.<BR>\n" );
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document.write( "solving as simultaneous equations works as follows:<BR>\n" );
document.write( "multiply x+y equation by 58<BR>\n" );
document.write( "2 equations become<BR>\n" );
document.write( "58*x + 52*y = 317<BR>\n" );
document.write( "58*x + 58*y = 58*5.75<BR>\n" );
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document.write( "subtracting the second equation from the first gets<BR>\n" );
document.write( "0*x + 52*y - 58*y = 317 - 58*5.75<BR>\n" );
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document.write( "the x has been eliminated and you are left with<BR>\n" );
document.write( "52*y - 58*y = 317 - 58*5.75<BR>\n" );
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document.write( "multiplying out and combining like terms gets<BR>\n" );
document.write( "-6*y = 317 - 333.5<BR>\n" );
document.write( "which becomes<BR>\n" );
document.write( "-6*y = -16.5<BR>\n" );
document.write( "which becomes<BR>\n" );
document.write( "-y = -2.75<BR>\n" );
document.write( "multiplying both sides by -1 and it becomes<BR>\n" );
document.write( "y = 2.75<BR>\n" );
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document.write( "since y = 2.75, and x + y = 5.75, then x = 3.0<BR>\n" );
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document.write( "you have<BR>\n" );
document.write( "x = 3.0<BR>\n" );
document.write( "y = 2.75<BR>\n" );
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document.write( "substituting in 58*x + 52*y = 317 gets<BR>\n" );
document.write( "58*3.0 + 52*2.75 = 317<BR>\n" );
document.write( "which becomes<BR>\n" );
document.write( "174 + 143 = 317<BR>\n" );
document.write( "which becomes<BR>\n" );
document.write( "317 = 317<BR>\n" );
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document.write( "answer is <BR>\n" );
document.write( "x = 3.0<BR>\n" );
document.write( "y = 2.75<BR>\n" );
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document.write( "if you did it the other way by taking x + y = 5.75 and solving for x, you would have gotten x = 5.75 - y.<BR>\n" );
document.write( "substituting in the other equation for x, you would have gotten<BR>\n" );
document.write( "58*(5.75-y) + 52*y = 317<BR>\n" );
document.write( "and you would have arrived at the same answer.<BR>\n" );
document.write( "-----\r<BR>\n" );
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document.write( " </SPAN>\n" );
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