document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=30688>Question 30688</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the time required to finish a mathematics test varies directly as the number of problems on the test and inversely as the number of hours spent studying. If a 50-problems test can be completed in 2 hours after 3 hours of studying, how long would a 75-problem test take after 4 hours of studying? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #17637 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=17637\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the solution by the other tutor is wrong.\r<BR>\n" );
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document.write( "Let T = time to finish<BR>\n" );
document.write( "let P = number of problems<BR>\n" );
document.write( "let H = number of hours of study\r<BR>\n" );
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document.write( "we are told 2 things:\r<BR>\n" );
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document.write( "T varies directly as P<BR>\n" );
document.write( "and <BR>\n" );
document.write( "T varies indirectly as H\r<BR>\n" );
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document.write( "Mathematically we have T proportinal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P%2FH+ ALIGN=MIDDLE  ALT=\"+P%2FH+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and hence \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+T+=+%28kP%29%2FH+ ALIGN=MIDDLE  ALT=\"+T+=+%28kP%29%2FH+\"   DISABLED_style= \"max-width:90%; height:auto;\" > where k is the constant of proportionality\r<BR>\n" );
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document.write( "So first we need to find the value of k, for which the question should supply all other variables:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2+=+%2850k%29%2F3+ ALIGN=MIDDLE  ALT=\"+2+=+%2850k%29%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--> 50k = 6<BR>\n" );
document.write( "--> k = 6/50<BR>\n" );
document.write( "--> k = 3/25\r<BR>\n" );
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document.write( "So, the formula is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+T+=+%283P%29%2F%2825H%29+ ALIGN=MIDDLE  ALT=\"+T+=+%283P%29%2F%2825H%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Now we can find the unknown, given the 2 values quoted.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+T+=+%283%2A75%29%2F%2825%2A4%29+ ALIGN=MIDDLE  ALT=\"+T+=+%283%2A75%29%2F%2825%2A4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+T+=+%28225%29%2F%28100%29+ ALIGN=MIDDLE  ALT=\"+T+=+%28225%29%2F%28100%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--> T = 2.25 Hours\r<BR>\n" );
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document.write( "or T = 2 hours 15 minutes\r<BR>\n" );
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document.write( "jon.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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