document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=155228>Question 155228</A>: <I><SPAN STYLE=\"word-break: break-all;\"> kindly solve these problems for me:<BR>\n" );
document.write( "1. Charles and Melanie are 100 km apart and are driving at constant speeds.  If they drive toward each other, they will meet in 1 hr.  If they drive in the same direction, he will overtake her in 5 hr.  Find their speeds.<BR>\n" );
document.write( "2. Wayne invested part of his money at 8% and the rest at 6%.  The income from both investments totaled $2,000.  If he interchanged his investments, his income would increase by $340.  How much did he have in each investment? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #114351 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=114351\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. Charles and Melanie are 100 km apart and are driving at constant speeds.<BR>\n" );
document.write( " If they drive toward each other, they will meet in 1 hr. If they drive in<BR>\n" );
document.write( " the same direction, he will overtake her in 5 hr. Find their speeds.<BR>\n" );
document.write( ";<BR>\n" );
document.write( "Let x = C's speed<BR>\n" );
document.write( "Let y = M's speed<BR>\n" );
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document.write( "When they are driving towards each other, their speeds are additive:<BR>\n" );
document.write( "Write a distance equation, Dist = time * speed<BR>\n" );
document.write( "1(x+y) = 100<BR>\n" );
document.write( "x + y = 100<BR>\n" );
document.write( "or<BR>\n" );
document.write( "y = (100-x)<BR>\n" );
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document.write( "Write another distance equation, when they go the same direction.<BR>\n" );
document.write( "C has to travel has to travel 100 further than M in the same time (5 hrs)\r<BR>\n" );
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document.write( "5x - 100 = 5y<BR>\n" );
document.write( "Replace y with (100-x)<BR>\n" );
document.write( "5x - 100 = 5(100-x)<BR>\n" );
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document.write( "5x - 100 = 500 - 5x<BR>\n" );
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document.write( "5x + 5x = 500 + 100<BR>\n" );
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document.write( "10x = 600<BR>\n" );
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document.write( "x = 60 km/hr is C's speed<BR>\n" );
document.write( "Find M's speed<BR>\n" );
document.write( "y = 100 - 60<BR>\n" );
document.write( "y = 40 km/hr is M's speed<BR>\n" );
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document.write( "Check solutions using the distance<BR>\n" );
document.write( "5*60 = 300 km<BR>\n" );
document.write( "5*40 = 200 km<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "diff = 100 km<BR>\n" );
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document.write( "2. Wayne invested part of his money at 8% and the rest at 6%. The income from <BR>\n" );
document.write( "both investments totaled $2,000. If he interchanged his investments, his<BR>\n" );
document.write( " income would increase by $340. How much did he have in each investment?<BR>\n" );
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document.write( "Originally: x = amt invested at 8% and y = amt invested at 6%<BR>\n" );
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document.write( ".08x + .06y = 2000; original income equation<BR>\n" );
document.write( ".06x + .08y = 2340; switched income equation<BR>\n" );
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document.write( "Multiply the 1st equation by 8, and the 2nd equation by 6; results<BR>\n" );
document.write( ".64x +.48y = 16000<BR>\n" );
document.write( ".36x + 48y = 14040<BR>\n" );
document.write( "----------------------subtraction eliminates y, find x<BR>\n" );
document.write( ".28x + 0y = 1960<BR>\n" );
document.write( ":<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1960%2F28 ALIGN=MIDDLE  ALT=\"1960%2F28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = $7,000 originally invested at 8%<BR>\n" );
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document.write( "Find y:<BR>\n" );
document.write( ".08(7000) + .06y = 2000<BR>\n" );
document.write( "560 + .06y = 2000<BR>\n" );
document.write( ".06y = 2000 - 560<BR>\n" );
document.write( ".06y = 1440<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1440%2F.06 ALIGN=MIDDLE  ALT=\"1440%2F.06\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y = $24,000<BR>\n" );
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document.write( "Check solution by switching the investments<BR>\n" );
document.write( ".08(24000) + .06(7000) =<BR>\n" );
document.write( "1920 + 420 = 2340; confirms our solutions<BR>\n" );
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document.write( ":<BR>\n" );
document.write( "Do you have any questions about either of these? did you understand what we did?\r<BR>\n" );
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document.write( " </SPAN>\n" );
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