document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=203971>Question 203971</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In an hour, Phoenix and Foghorn have munched all of the viral bodies. Phoenix, never one to miss a meal, can eat the same amount of virus by itself. Foghorn, the dainter of the two phagoes, can eat the same amount of virus as its twin, but it takes 25 minutes longer.\r<BR>\n" );
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document.write( "If phoenix dined alone how long would it take to consume the viral load? How long would it take Foghorn?\r<BR>\n" );
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document.write( "Im kinda lost on this one. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #153921 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=153921\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> took a while because i'm a little rusty, but i think i have the answer.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "let p = the rate at which phoenix eats virus.<BR>\n" );
document.write( "let f = the rate at which foghorn eats virus.<BR>\n" );
document.write( "eating together, they can consume all of the virus in 1 hours.<BR>\n" );
document.write( "since 1 hour = 60 minutes, we can use minutes rather than hours.<BR>\n" );
document.write( "----<BR>\n" );
document.write( "our equation we have to work with is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60+%2A+%28f+%2B+p%29+=+v ALIGN=MIDDLE  ALT=\"60+%2A+%28f+%2B+p%29+=+v\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2Af+%2B+60%2Ap+=+v ALIGN=MIDDLE  ALT=\"60%2Af+%2B+60%2Ap+=+v\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "we know that eating alone phoenix can consume the virus in t minutes.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "t is a small letter T not to be confused with the + sign if at all possible.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "our formula for phoenix eating the virus alone is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2Ap+=+v ALIGN=MIDDLE  ALT=\"t%2Ap+=+v\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "we know that eating alone foghorn can consume the virus in t+25 minutes.<BR>\n" );
document.write( "our formula for foghorn eating the virus alone is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28t%2B25%29%2Af+=+v ALIGN=MIDDLE  ALT=\"%28t%2B25%29%2Af+=+v\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "we can solve for p and f in terms of v and t.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+v%2Ft ALIGN=MIDDLE  ALT=\"p+=+v%2Ft\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f+=+v%2F%28t%2B25%29 ALIGN=MIDDLE  ALT=\"f+=+v%2F%28t%2B25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "our equation that we had above of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2Af+%2B+60%2Ap+=+v ALIGN=MIDDLE  ALT=\"60%2Af+%2B+60%2Ap+=+v\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60+%2A+%28v%2Ft%29+%2B+60+%2A+%28v%2F%28t%2B25%29%29+=+v ALIGN=MIDDLE  ALT=\"60+%2A+%28v%2Ft%29+%2B+60+%2A+%28v%2F%28t%2B25%29%29+=+v\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "if we divide both sides of this equation by v, then the v cancels out and we are left with:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2Ft+%2B+60%2F%28t%2B25%29+=+1 ALIGN=MIDDLE  ALT=\"60%2Ft+%2B+60%2F%28t%2B25%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "if we multiply both sides of this equation by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2A%28t%2B25%29 ALIGN=MIDDLE  ALT=\"t%2A%28t%2B25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2A%28t%2B25%29+%2B+60%2At+=+t%2A%28t%2B25%29 ALIGN=MIDDLE  ALT=\"60%2A%28t%2B25%29+%2B+60%2At+=+t%2A%28t%2B25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "that equation becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2At+%2B+25%2A60+%2B+60%2At+=+t%5E2+%2B+25%2At ALIGN=MIDDLE  ALT=\"60%2At+%2B+25%2A60+%2B+60%2At+=+t%5E2+%2B+25%2At\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which becomes<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120%2At+%2B+1500+=+t%5E2+%2B+25%2At ALIGN=MIDDLE  ALT=\"120%2At+%2B+1500+=+t%5E2+%2B+25%2At\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "if we subtract 120*t + 1500 from both sides of the equation, we are left with:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2+-+95%2At+-+1500+=+0 ALIGN=MIDDLE  ALT=\"t%5E2+-+95%2At+-+1500+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "i used the quadratic formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-b+%2B-+sqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"%28-b+%2B-+sqrt%28b%5E2-4ac%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to solve this.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "i got:<BR>\n" );
document.write( "t = 108.7882534<BR>\n" );
document.write( "and<BR>\n" );
document.write( "t = -13.78825336 which was rejected because it's negative.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "my answer was t = 108.7882534<BR>\n" );
document.write( "this made (t+25) = 133.7882534<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the question to be answered was:<BR>\n" );
document.write( "If phoenix dined alone how long would it take to consume the viral load? How long would it take Foghorn?<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "t is the time it takes phoenix to eat the virus.<BR>\n" );
document.write( "t+25 is the time it takes foghorn to eat the virus.<BR>\n" );
document.write( "your answers are:<BR>\n" );
document.write( "it takes phoenix 108.7882534 minutes to eat the virus.<BR>\n" );
document.write( "it takes foghorn 133.7882534 minutes to eat the virus.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the rate that phoenix takes to eat the virus is v/108.7882534 = p<BR>\n" );
document.write( "the rate that foghorn takes to eat the virus is v/133.7882534 = f<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "to prove your answer is correct, substitute in the original equation to see if you get the right answer.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the original equation is 60 * (f + p) = v<BR>\n" );
document.write( "this becomes 60 * (v/108.7882534 + v/133.7882534) = v<BR>\n" );
document.write( "this becomes (60*v)/108.7882534 + (60*v)/133.7882534 = v<BR>\n" );
document.write( "divide both sides of this equation by v and you get:<BR>\n" );
document.write( "(60/108.7882534 + 60/133.7882534 = 1<BR>\n" );
document.write( "which becomes:<BR>\n" );
document.write( ".551530134 + .448469866 = 1<BR>\n" );
document.write( "which becomes:<BR>\n" );
document.write( "1 = 1<BR>\n" );
document.write( "original equation is true so the answer are good.<BR>\n" );
document.write( "your answers again are:<BR>\n" );
document.write( "it takes phoenix 108.7882534 minutes to eat the virus.<BR>\n" );
document.write( "it takes foghorn 133.7882534 minutes to eat the virus.<BR>\n" );
document.write( "-----\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );