document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1037381>Question 1037381</A>: <I><SPAN STYLE=\"word-break: break-all;\"> josie can type 100 words in the same time that it take jane to type 75 word. if jane's typing rate is 8 words per minute less than that of josie's, find jane's typing rate </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #652053 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=652053\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let a = the typing rate of josie<BR>\n" );
document.write( "let b = the typing rate of jane<BR>\n" );
document.write( "let x = the time it takes for each of them to finish typing.<BR>\n" );
document.write( "this means that josie takes x minutes to type 100 words.<BR>\n" );
document.write( "this means that jane takes x minutes to type 75 words.\r<BR>\n" );
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document.write( "the general formula is rate * time = quantity.\r<BR>\n" );
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document.write( "for josie, this equation becomes a * x = 100<BR>\n" );
document.write( "for jane, this equation becomes b * x = 75\r<BR>\n" );
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document.write( "solve both equations for x and you get:\r<BR>\n" );
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document.write( "x = 100/a<BR>\n" );
document.write( "x = 75/b\r<BR>\n" );
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document.write( "this means that 100/a = 75/b<BR>\n" );
document.write( "cross multiply to get 100b = 75a<BR>\n" );
document.write( "solve for b to get b = 75a/100 which simplifies to b = 3/4 * a\r<BR>\n" );
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document.write( "you are given that b = a - 8.<BR>\n" );
document.write( "replace b with a-8 in this equation to get a-8 = 3/4 * a<BR>\n" );
document.write( "add 8 to both sides of this equation and subtract 3/4 * a from both sides of this equation to get a - 3/4 * a = 8<BR>\n" );
document.write( "simplify to get 1/4 * a = 8<BR>\n" );
document.write( "multiply both sides of this equation by 4 to get a = 32.\r<BR>\n" );
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document.write( "since b = a-8, you get:\r<BR>\n" );
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document.write( "a = 32<BR>\n" );
document.write( "b = 24\r<BR>\n" );
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document.write( "since b = jane's typing rate, your answer is that ....\r<BR>\n" );
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document.write( "jane's typing rate is 24 words per minute.\r<BR>\n" );
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document.write( "you can confirm the answer is correct since they both took the same time.\r<BR>\n" );
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document.write( "rate * time = quantity\r<BR>\n" );
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document.write( "for josie, this means 32 * time = 100.<BR>\n" );
document.write( "for jane, this means 24 * time = 75\r<BR>\n" );
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document.write( "solve for time in each equation and you get:\r<BR>\n" );
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document.write( "for josie, time = 100 / 32 = 25 / 8.<BR>\n" );
document.write( "for jane, time = 75 / 24 = 25 / 8.\r<BR>\n" );
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document.write( "the time is the same, confirming the solution is correct.\r<BR>\n" );
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document.write( "there was another way to solve this as well.\r<BR>\n" );
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document.write( "same setup.\r<BR>\n" );
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document.write( "ax = 100<BR>\n" );
document.write( "bx = 75\r<BR>\n" );
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document.write( "subtract the second equation from the first to get ax - bx = 25<BR>\n" );
document.write( "factor out the x to get (a-b)x = 25<BR>\n" );
document.write( "solve for x to get x = 25/(a-b)\r<BR>\n" );
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document.write( "you are given that b = a-8.<BR>\n" );
document.write( "replace b in the equation to get x = 25/(a - (a-8))<BR>\n" );
document.write( "simplify to get x = 25/8.\r<BR>\n" );
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document.write( "now that you know the time, you can solve for a and b.\r<BR>\n" );
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document.write( "a * 25/8 = 100<BR>\n" );
document.write( "a * 25 = 8*100<BR>\n" );
document.write( "a = 8*100/25 = 8*4 = 32\r<BR>\n" );
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document.write( "b * 25/8 = 75<BR>\n" );
document.write( "b * 25 = 8*75<BR>\n" );
document.write( "b = 8*75/25 = 8*3 = 24\r<BR>\n" );
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document.write( "you get the same answer either way.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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