document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1175277>Question 1175277</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Practice Age word  Problem\r<BR>\n" );
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document.write( "Ariana started biking to the library traveling 14 mph, after some time the bike got a flat so Ariana walked the rest of the way, traveling 7 mph. If the total trip to the library took 11 hours and it was 119 miles away, how long did Ariana travel at each speed? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #800927 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=800927\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "You have received two response showing similar formal algebraic solutions.<br><BR>\n" );
document.write( "Here is a very different path to the answer that I personally find much faster and easier (if a formal algebraic solution is not required).<br><BR>\n" );
document.write( "This is essentially a mixture problem -- you are mixing some number of hours at 14mph with some number of hours at 7mph and ending up with a total of 119 miles in 11 hours.<br><BR>\n" );
document.write( "You can solve any two-part mixture problem like that in the following way.<br><BR>\n" );
document.write( "All 11 hours at 7mph would cover 77 miles<BR>\n" );
document.write( "All 11 hours at 14mph would cover 154 miles<BR>\n" );
document.write( "The actual distance covered was 119 miles<br><BR>\n" );
document.write( "Look at the three mileage totals on a number line; with simple calculations, determine that 119 is 42/77 = 6/11 of the way from 77 to 154.<BR>\n" );
document.write( "That means 6/11 of the total time was at the higher rate.<BR>\n" );
document.write( "6/11 of 11 hours is 6 hours.<br><BR>\n" );
document.write( "ANSWER: 6 hours at 14mph/ 5 hours at 7mph<br><BR>\n" );
document.write( "CHECK: 6(14)+5(7) = 84+35 = 119<br><BR>\n" );
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