document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=30487>Question 30487</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could you tell me if I've presented this in the right way:<BR>\n" );
document.write( "Next-door neighbors Bob and Jim use hoses from both houses to fill Bob's swimming pool. They know it takes 18 hours using both hoses. They also know that Bob's hose, used alone, takes 20% less time than Jim's hose alone. How much time is required to fill the pool by each hose alone?\r<BR>\n" );
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document.write( "let x = the faster hose<BR>\n" );
document.write( "let .8x = the slower hose (80% capacity)<BR>\n" );
document.write( "then<BR>\n" );
document.write( "x+ .8x = 18<BR>\n" );
document.write( "1.8x = 18<BR>\n" );
document.write( "x = 10 hours for the faster hose<BR>\n" );
document.write( ".8(10) 8 hours for the slower hose<BR>\n" );
document.write( "= 18 total hours for both.\r<BR>\n" );
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document.write( "Thanks for all your help!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #17235 by </B><A HREF=/tutors/aboutme.mpl?userid=mbarugel><B>mbarugel(146)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mbarugel><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=17235\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hello!<BR>\n" );
document.write( "There's a mistake in your solution. You know that it takes 18 hours using both hoses at the same time, but this is more time than what you found for each hose separately. If 2 hoses at the same time filled the pool in 18 hours, then each of them on their own should take MORE than 18 hours instead of 8 or 10. Here's how to solve this.\r<BR>\n" );
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document.write( "Let's call X to the number of hours it takes for the \"slow\" hose to fill the pool on its own. Therefore, the \"fast\" hose takes 0.8X hours to fill the pool on its own. Notice that this implies the following:\r<BR>\n" );
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document.write( "- The slow hose fills a fraction 1/X of the pool per hour (for example, if it takes 10 hours to fill the pool, it fills 1/10 of the pool per hour)\r<BR>\n" );
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document.write( "- The fast hose filles a fraction 1/(0.8X) of the pool per hour.\r<BR>\n" );
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document.write( "- Therefore, the two hoses at the same time fill a fraction <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2FX%2B1%2F%280.8X%29 ALIGN=MIDDLE  ALT=\"1%2FX%2B1%2F%280.8X%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the pool per hour. But we also know that it takes 18 hours for both to fill the pool. So we have the equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2FX%2B1%2F%280.8X%29+=+1%2F18 ALIGN=MIDDLE  ALT=\"1%2FX%2B1%2F%280.8X%29+=+1%2F18\"   DISABLED_style= \"max-width:90%; height:auto;\" > (since it takes 18 hours, they fill 1/18 per hour)\r<BR>\n" );
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document.write( "And now it's just a matter of isolating X from this equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2FX%29%281%2B1%2F0.8%29+=+1%2F18 ALIGN=MIDDLE  ALT=\"%281%2FX%29%281%2B1%2F0.8%29+=+1%2F18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2FX%292.25+=+1%2F18 ALIGN=MIDDLE  ALT=\"%281%2FX%292.25+=+1%2F18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2FX%292.25+=+1%2F18 ALIGN=MIDDLE  ALT=\"%281%2FX%292.25+=+1%2F18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2A2.25+=+X ALIGN=MIDDLE  ALT=\"18%2A2.25+=+X\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X+=+40.5 ALIGN=MIDDLE  ALT=\"X+=+40.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the slow hose takes 40.5 hours on its own to fill the pool. The fast hose takes 0.8*40.5 = 32.4 hours.\r<BR>\n" );
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document.write( "I hope this helps!\r<BR>\n" );
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document.write( "Get more answers at <a  rel=nofollow HREF=http://www.onlinemathanswers.com>Online Math Answers.com</a>! </SPAN>\n" );
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