document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189020>Question 1189020</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. Train A has a speed 20 miles per hour greater than that of train B. If train A travels 300 miles in the same times train B travels 220 miles, what are the speeds of the two trains?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2. A woman has a total of $13,000 to invest. She invests part of the money in an account that pays 11% per year and the rest in an account that pays 12% per year. If the interest earned in the first year is $1490 how much did she invest in each account?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #820248 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=820248\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. The difference in speeds of the two trains is 20mph; the difference in distances over the same amount of time is 80 miles.  So the time traveled is 80/20 = 4 hours.<br><BR>\n" );
document.write( "Train A travels 300 miles in 4 hours, a speed of 75mph; train B travels 220 miles in 4 hours, a speed of 55mph.<br><BR>\n" );
document.write( "ANSWERS: 75 and 55mph<br><BR>\n" );
document.write( "2. Here is an informal method for solving \"mixture\" problems like this that is nearly always faster and easier than the standard formal algebraic method shown by the other tutor.<br><BR>\n" );
document.write( "(a) All $13,000 invested at 11% would yield $1430 interest; all invested at 12% would yield $1560 interest.<BR>\n" );
document.write( "(b) View the three interest amounts $1430, $1490, and $1560 on a number line and observe/calculate that $1490 is $60/$130 = 6/13 of the way from $1430 to $1560.<BR>\n" );
document.write( "(c) That means 6/13 of the total was invested at the higher rate.<br><BR>\n" );
document.write( "6/13 of $13,000 is $6000, so<br><BR>\n" );
document.write( "ANSWERS: $6000 invested at 12%, the other $7000 at 11%<br><BR>\n" );
document.write( "CHECK: .12(6000)+.11(7000) =720+770=1490<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );