document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=992308>Question 992308</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Tammy and Cheryl are building a bridge over a small river. Tammy can do the job alone in 24 hours. Cheryl can do the job alone in 28 hours. Tammy worked on the project alone 4 hours before Cheryl joined her. The two then finished the job together. How long did it take the two to finish the job that Tammy had started alone. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #611932 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=611932\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Tammy can do the job in 24 hours.<BR>\n" );
document.write( "her rate is therefore 1/24 of the job in one hour.\r<BR>\n" );
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document.write( "Cheryl can do the job in 28 hours.<BR>\n" );
document.write( "her rate is therefore 1/28 of the job in one hour.\r<BR>\n" );
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document.write( "this is because rate * time = quantity.\r<BR>\n" );
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document.write( "quantity is equal to 1 because they are building 1 bridge.\r<BR>\n" );
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document.write( "for Tammy, this equation becomes rate * 24 = 1 which gets rate = 1/24.<BR>\n" );
document.write( "for Cheryl, this equation becomes rate * 28 = 1 which gets rate = 1/28.\r<BR>\n" );
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document.write( "Tammy works alone for 4 hours.\r<BR>\n" );
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document.write( "at a rate of 1/24 of the bridge in 1 hour, she completes 4/24 of the bridge in 4 hours.\r<BR>\n" );
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document.write( "this leaves 20/24 of the bridge remaining to be completed.\r<BR>\n" );
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document.write( "working together, their rates are additive, so you get:\r<BR>\n" );
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document.write( "(1/24 + 1/28) * time = 20/24\r<BR>\n" );
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document.write( "simplfy this to get 1/24 * time + 1/28 * time = 20/24.\r<BR>\n" );
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document.write( "multiply both sides of the equation by 24 * 28 to get:\r<BR>\n" );
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document.write( "28 * time + 24 * time = 20/24 * 24 * 28\r<BR>\n" );
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document.write( "combine like terms on the left and simplify on the right to get:\r<BR>\n" );
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document.write( "52 * time = 20 * 28\r<BR>\n" );
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document.write( "divide both sides of this equation by 52 and solve for time to get:\r<BR>\n" );
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document.write( "time = (20 * 28) / 52.\r<BR>\n" );
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document.write( "simplify this fraction to get:\r<BR>\n" );
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document.write( "time = (5 * 28) / 13\r<BR>\n" );
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document.write( "this simplifies further to get:\r<BR>\n" );
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document.write( "time = 140 / 13 hours.\r<BR>\n" );
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document.write( "that's equivalent to 10 and 10/13 hours.\r<BR>\n" );
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document.write( "the decimal equivalent of that would be time = 10.7692307692... hours.\r<BR>\n" );
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document.write( "fractional form is an exact answer.<BR>\n" );
document.write( "decimal form is an approximaton.\r<BR>\n" );
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document.write( "4/24 of the job that Tammy finished alone and 20/24 of the job that Tammy and Cheryl finished together took 4 hours plus 10 and 10/13 hours for a total of 14 and 10/13 hours.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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