document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=41752>Question 41752</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Rational equations <BR>\n" );
document.write( "Juanelda’s doctor has prescribed medication that she must take every 5 hours. She started the medication at 10:00am on Thursday. What is the first day on which she will take her medication at noon? Write an equation that will prove this answer.<BR>\n" );
document.write( "Thank you. <BR>\n" );
document.write( "OK SO I THINK ITS ON A SATERDAY BUT I DONT KNOW HOW TO WRITE AN EQUATION TO PROVE THIS ANSWER.<BR>\n" );
document.write( "I JUST WENT 10:00AM THURSDAY, 3:00PM tHURSDAY, 8:00PM THURSDAY, 1:00AM FRIDAY, 6:00AM FRIDAY, 11:00AM FRIDAY, 4:00PM FRIDAY, 9:00PM FRIDAY, 2:00AM SATERDAY, 7:00AM SATERDAY, 12:00PM NOON SATERDAY </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #26958 by </B><A HREF=/tutors/aboutme.mpl?userid=psbhowmick><B>psbhowmick(878)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=psbhowmick><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=psbhowmick><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=26958\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let us count time from Thursday 0 (zero) hrs.<BR>\n" );
document.write( "Let us denote the time at which she will take her first medication at noon, counted from 0 hrs Thursday, be 't' hours.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So 't' must be an integral multiple of 12 but not an integral multiple of 24 (for in that case it will be 12pm i.e. night and not noon).<BR>\n" );
document.write( "So let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+12%2Am ALIGN=MIDDLE  ALT=\"t+=+12%2Am\"   DISABLED_style= \"max-width:90%; height:auto;\" > where m = an odd positive integer (as 't' cannot be a multiple of 24)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Further, suppose that her first medication at noon is actually her n-th medication.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Then, the time elapsed counted from 10 am Thursday upto that when she takes her first medication at noon is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%28n-1%29 ALIGN=MIDDLE  ALT=\"5%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Then, the time elapsed counted from 0 hrs Thursday upto that when she takes her first medication at noon is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%28n-1%29%2B10 ALIGN=MIDDLE  ALT=\"5%28n-1%29%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Thus we can write, t = 5(n - 1) + 10<BR>\n" );
document.write( "or 12m = 5(n + 1)<BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2B1+=+12m%2F5 ALIGN=MIDDLE  ALT=\"n%2B1+=+12m%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+12m%2F5+-+1 ALIGN=MIDDLE  ALT=\"n+=+12m%2F5+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now, 'n' = no. of times of occurance of an event, so has to be a positive whole number.<BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12m%2F5-1 ALIGN=MIDDLE  ALT=\"12m%2F5-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > has got to be positive integer or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12m%2F5 ALIGN=MIDDLE  ALT=\"12m%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > has got to be positive integer.<BR>\n" );
document.write( "Also 'm' can attain only odd integral values and 'm' has to be least among all the values of 'm' for which the above equation holds (This is because otherwise n-th time will not be the first time of medication at noon). <BR>\n" );
document.write( "So we take m = 5, n = 11;\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Thus, 11th medication is the first one done at noon.<BR>\n" );
document.write( "Now, t = 12 x 5 = 60 = 2 x 24 + 12.<BR>\n" );
document.write( "So 2 and a half day has elapsed (from Thursday 0 hrs) when the girl takes her first medication at noon.<BR>\n" );
document.write( "Hence the answer. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );