document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=607978>Question 607978</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone please help me solve this word problem. I'm studying on Fractional Equations and Problem Solving. Thank you! \r<BR>\n" );
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document.write( "In a survivor competition, the Pachena tribe can shuck 300 oysters in 10 minutes less time than it takes the Tchaika tribe. If the Pachena tribe shucks oysters at a rate of 5 oysters per minute faster than the Tchaika tribe, find the rate of each tribe. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #382983 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=382983\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In a survivor competition, the Pachena tribe can shuck 300 oysters in 10 minutes less time than it takes the Tchaika tribe.<BR>\n" );
document.write( " If the Pachena tribe shucks oysters at a rate of 5 oysters per minute faster than the Tchaika tribe, find the rate of each tribe.<BR>\n" );
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document.write( "Let p = time for the P tribe to shuck 300 oyster<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(p+10) = time for T tribe to do it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300%2Fp ALIGN=MIDDLE  ALT=\"300%2Fp\"   DISABLED_style= \"max-width:90%; height:auto;\" > = oysters/min of the P tribe<BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300%2F%28%28p%2B10%29%29 ALIGN=MIDDLE  ALT=\"300%2F%28%28p%2B10%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = oysters/min of the T tribe<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write an equation for the statement:<BR>\n" );
document.write( "\"the Pachena tribe shucks oysters at a rate of 5 oysters per minute faster than the Tchaika tribe,\"<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300%2Fp ALIGN=MIDDLE  ALT=\"300%2Fp\"   DISABLED_style= \"max-width:90%; height:auto;\" > - 5 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300%2F%28%28p%2B10%29%29 ALIGN=MIDDLE  ALT=\"300%2F%28%28p%2B10%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "multiply by p(p+10), resulting in<BR>\n" );
document.write( "300(p+10) - 5p(p+10) = 300p<BR>\n" );
document.write( "300p + 3000 - 5p^2 - 50p = 300p<BR>\n" );
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document.write( "Combine like terms on the right<BR>\n" );
document.write( "0 = 5p^2 +50p +300p - 300p - 3000<BR>\n" );
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document.write( "A quadratic equation<BR>\n" );
document.write( "5p^2 + 50p - 3000 = 0<BR>\n" );
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document.write( "simplify, divide by 5<BR>\n" );
document.write( "p^2 + 10p - 600 = 0<BR>\n" );
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document.write( "Factors to <BR>\n" );
document.write( "(p+30)(p-20) = 0<BR>\n" );
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document.write( "the positive solution<BR>\n" );
document.write( "p = 20 min to shuck 300 oysters<BR>\n" );
document.write( "then<BR>\n" );
document.write( "20 + 10 = 30 min to shuck 300 oysters per min for the T tribe<BR>\n" );
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document.write( "Find the rates<BR>\n" );
document.write( "300/20 = 15 oysters/min<BR>\n" );
document.write( "300/30 = 10 oysters/min, a difference of 5 per min<BR>\n" );
document.write( " </SPAN>\n" );
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