document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202341>Question 1202341</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Rosie ran to the park at 7 miles per hour and walked back home at 3 miles per hour. How many miles was it to the park if the round trip took 20 hours? Begin by drawing a diagram of distances traveled and writing the distance equation on your paper. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #837094 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=837094\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Answer:  <font color=red size=4>42 miles</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "====================================================================================\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Explanation:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = distance, in miles, from Rosie's house to the park.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Draw a rough sketch of what's going on.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C300%2C-4%2C4%2C-2%2C5%2C%0D%0Aline%28-3%2C0%2C3%2C0%29%2C%0D%0Acircle%28-3%2C0%2C0.04%29%2C%0D%0Acircle%28-3%2C0%2C0.06%29%2C%0D%0Acircle%28-3%2C0%2C0.08%29%2C%0D%0Acircle%28-3%2C0%2C0.10%29%2C%0D%0Acircle%283%2C0%2C0.04%29%2C%0D%0Acircle%283%2C0%2C0.06%29%2C%0D%0Acircle%283%2C0%2C0.08%29%2C%0D%0Acircle%283%2C0%2C0.10%29%2C%0D%0Alocate%28-3-0.5%2C0-0.1%2C%22Home%22%29%2C%0D%0Alocate%283%2C0-0.1%2C%22Park%22%29%2C%0D%0Alocate%280%2C0-0.1%2Cmatrix%281%2C2%2C%22x%22%2C%22miles%22%29%29%2C%0D%0Aline%28-3%2C1%2C3%2C1%29%2Cline%283%2C1%2C2.4804%2C0.7%29%2Cline%283%2C1%2C2.4804%2C1.3%29%2C%0D%0Aline%283%2C2%2C-3%2C2%29%2Cline%28-3%2C2%2C-2.4804%2C2.3%29%2Cline%28-3%2C2%2C-2.4804%2C1.7%29%2C%0D%0Alocate%28-0.5%2C1.5%2Cmatrix%281%2C3%2C%22Running%3A%22%2C%227%22%2C%22mph%22%29%29%2C+%0D%0Alocate%28-0.5%2C2.5%2Cmatrix%281%2C3%2C%22Walking%3A%22%2C%223%22%2C%22mph%22%29%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Here's a table to organize the knowns and unknowns so far.<BR>\n" );
document.write( "<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD ></TD><TD >Distance (miles)</TD><TD >Rate (mph)</TD><TD >Time (hrs)</TD></tr><tr><TD >Running</TD><TD >x</TD><TD >7</TD><TD >x/7</TD></tr><tr><TD >Walking</TD><TD >x</TD><TD >3</TD><TD >x/3</TD></tr>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "Relevant formulas:<BR>\n" );
document.write( "Distance = rate*time<BR>\n" );
document.write( "time = distance/rate\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The two time values x/7 and x/3 must add to the grand total of 20 hours. This is the round trip time.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "time1+time2 = round trip time<BR>\n" );
document.write( "x/7 + x/3 = 20<BR>\n" );
document.write( "21*(x/7 + x/3) = 21*20<BR>\n" );
document.write( "21*(x/7) + 21*(x/3) = 420<BR>\n" );
document.write( "3x + 7x = 420<BR>\n" );
document.write( "10x = 420<BR>\n" );
document.write( "x = 420/10<BR>\n" );
document.write( "x = 42\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The distance from her home to the park is <font color=red>42 miles</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "She runs at 7 mph, so she took x/7 = 42/7 = 6 hours to run to the park.<BR>\n" );
document.write( "Rosie walks at 3 mph. She took x/3 = 42/3 = 14 hours to walk back home.<BR>\n" );
document.write( "That's a total of 6+14 = 20 hours to verify we have the correct answer.<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );