document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=174973>Question 174973</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help!!<BR>\n" );
document.write( "- A car travelled 470 km from Sudbury to Brandford in 5 hours. For part of the trip, the car travelled at 100 km/h. For the rest of the trip, it travelled at 90 km/h. How far did the car travel at each speed?\r<BR>\n" );
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document.write( "I tried <BR>\n" );
document.write( "x+y=5<BR>\n" );
document.write( "100x+90=470\r<BR>\n" );
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document.write( "100x+100y=500<BR>\n" );
document.write( "100x+90y=470\r<BR>\n" );
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document.write( "= 10y = 30<BR>\n" );
document.write( "x=2 y=3<BR>\n" );
document.write( "but I only got half marks. Where did I go wrong and what was the answer? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #130041 by </B><A HREF=/tutors/aboutme.mpl?userid=Electrified_Levi><B>Electrified_Levi(103)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Electrified_Levi><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=130041\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi, Hope I can help,<BR>\n" );
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document.write( "I need help!!<BR>\n" );
document.write( "- A car travelled 470 km from Sudbury to Brandford in 5 hours. For part of the trip, the car travelled at 100 km/h. For the rest of the trip, it travelled at 90 km/h. How far did the car travel at each speed? <BR>\n" );
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document.write( "We will start fresh<BR>\n" );
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document.write( "First we need to know a formula<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28rate%29%28time%29=+distance+ ALIGN=MIDDLE  ALT=\"+%28rate%29%28time%29=+distance+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or with abbreviations, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%29%28t%29+=+d+ ALIGN=MIDDLE  ALT=\"+r%29%28t%29+=+d+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "A car travelled 470 km from Sudbury to Brandford in 5 hours. For part of the trip, the car travelled at 100 km/h. For the rest of the trip, it travelled at 90 km/h. How far did the car travel at each speed? <BR>\n" );
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document.write( "This problem is a little tricky, since the car is going two speeds, instead of just one, we also have two different times.<BR>\n" );
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document.write( "This will mean we will have two unknowns, we can find the other unknowns with the information we have<BR>\n" );
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document.write( "A car travelled 470 km from Sudbury to Brandford in 5 hours. For part of the trip, the car travelled at 100 km/h. For the rest of the trip, it travelled at 90 km/h. How far did the car travel at each speed?<BR>\n" );
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document.write( "Remember that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+rate%28time%29+=+distance+ ALIGN=MIDDLE  ALT=\"+rate%28time%29+=+distance+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we don't know the time or distance for either one of the speeds, but we know the total distance and total time<BR>\n" );
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document.write( "We can say that the time it took when the car went 90 km/h, the time it took would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+ ALIGN=MIDDLE  ALT=\"+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We can say that how long it took when the car went 100 km/h, the time it took would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5+-+x+ ALIGN=MIDDLE  ALT=\"+5+-+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, ( if you subtract the other time, from the total time, you will find the second unknown time )<BR>\n" );
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document.write( "It is the same concept with the distances<BR>\n" );
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document.write( "one distance would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+ ALIGN=MIDDLE  ALT=\"+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "the second unknown distance would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+470+-+y+ ALIGN=MIDDLE  ALT=\"+470+-+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We can now find equations to this problem<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%28t%29+=+d+ ALIGN=MIDDLE  ALT=\"+r%28t%29+=+d+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Equation 1<BR>\n" );
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document.write( "if the car went 100 km/h ( rate )<BR>\n" );
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document.write( "if the car took <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5+-+x+ ALIGN=MIDDLE  ALT=\"+5+-+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > hours ( time ), ( doesn't matter which time we could use \"x\" if we wanted, but we will use this one )<BR>\n" );
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document.write( "These two multiplied together will equal a distance <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+470+-+y+ ALIGN=MIDDLE  ALT=\"+470+-+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" > , ( once again it doen't matter which distance, we could use \"y\" if we wanted )<BR>\n" );
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document.write( "Now we would put the words into a formula,<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+rate%28time%29=+distance+ ALIGN=MIDDLE  ALT=\"+rate%28time%29=+distance+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+100%285+-+x%29+=+470+-+y+ ALIGN=MIDDLE  ALT=\"+100%285+-+x%29+=+470+-+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this is the first equation<BR>\n" );
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document.write( "Now we will use the other distance, time, and rate, to find the second equation<BR>\n" );
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document.write( "If the car went 90 km/h ( rate )<BR>\n" );
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document.write( "If the car took <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+ ALIGN=MIDDLE  ALT=\"+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > hours ( time )<BR>\n" );
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document.write( "If the car drove <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+ ALIGN=MIDDLE  ALT=\"+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" > km ( distance )<BR>\n" );
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document.write( "Now replace \"r\", \"t\" and \"d\" with the other veriables<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%28t%29+=+d+ ALIGN=MIDDLE  ALT=\"+r%28t%29+=+d+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+90%28x%29+=+y+ ALIGN=MIDDLE  ALT=\"+90%28x%29+=+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this is the second equation<BR>\n" );
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document.write( "Now we can put these two equations side by side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system+%28+100%285+-+x%29+=+470+-+y%2C+90%28x%29+=+y%29+ ALIGN=MIDDLE  ALT=\"+system+%28+100%285+-+x%29+=+470+-+y%2C+90%28x%29+=+y%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "To make it easier, we will simplify the two equations<BR>\n" );
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document.write( "Equation 1, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+100%285+-+x%29+=+470+-+y+ ALIGN=MIDDLE  ALT=\"+100%285+-+x%29+=+470+-+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can use the distribution to simplify this equation<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+100%285+-+x%29+=+470+-+y+ ALIGN=MIDDLE  ALT=\"+100%285+-+x%29+=+470+-+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%28100%29%28highlight%285%29+-+x%29+=+470+-+y+ ALIGN=MIDDLE  ALT=\"+highlight%28100%29%28highlight%285%29+-+x%29+=+470+-+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%28100%29%285+-+highlight%28x%29%29+=+470+-+y+ ALIGN=MIDDLE  ALT=\"+highlight%28100%29%285+-+highlight%28x%29%29+=+470+-+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(remember the signs<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+100%285%29+-+100%28x%29+=+470+-+y+ ALIGN=MIDDLE  ALT=\"+100%285%29+-+100%28x%29+=+470+-+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+500+-+100x+=+470+-+y+ ALIGN=MIDDLE  ALT=\"+500+-+100x+=+470+-+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we don't have to move anything right now, so this is the simplified form<BR>\n" );
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document.write( "Equation 2, we will just multiply the \"90\" and \"x\"<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+90%28x%29+=+y+ ALIGN=MIDDLE  ALT=\"+90%28x%29+=+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+90x+=+y+ ALIGN=MIDDLE  ALT=\"+90x+=+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this is simplified<BR>\n" );
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document.write( "Now we can start solving for the two unknowns<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system+%28+500+-+100x+=+470+-+y%2C+90x+=+y%29+ ALIGN=MIDDLE  ALT=\"+system+%28+500+-+100x+=+470+-+y%2C+90x+=+y%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This is a system of equations, the easiest way to solve this system is by substitution<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+90x+ ALIGN=MIDDLE  ALT=\"+y+=+90x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can just simply replace \"y\" in the first equation with \"90x\"<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+500+-+100x+=+470+-+y+ ALIGN=MIDDLE  ALT=\"+500+-+100x+=+470+-+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+500+-+100x+=+470+-+%2890x%29+ ALIGN=MIDDLE  ALT=\"+500+-+100x+=+470+-+%2890x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+500+-+100x+=+470+-+%2890x%29+ ALIGN=MIDDLE  ALT=\"+500+-+100x+=+470+-+%2890x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+500+-+100x+=+470+-+90x+ ALIGN=MIDDLE  ALT=\"+500+-+100x+=+470+-+90x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, now we can just solve for \"x\", we will move (-100x) to the right side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+500+-+100x+=+470+-+90x+ ALIGN=MIDDLE  ALT=\"+500+-+100x+=+470+-+90x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+500+-+100x+%2B+100x+=+470+-+90x+%2B+100x+ ALIGN=MIDDLE  ALT=\"+500+-+100x+%2B+100x+=+470+-+90x+%2B+100x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+500+=+470+%2B+10x+ ALIGN=MIDDLE  ALT=\"+500+=+470+%2B+10x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, now we will move \"470\" to the left side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+500+=+470+%2B+10x+ ALIGN=MIDDLE  ALT=\"+500+=+470+%2B+10x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+500+-+470+=+470+-+470+%2B+10x+ ALIGN=MIDDLE  ALT=\"+500+-+470+=+470+-+470+%2B+10x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+30+=+10x+ ALIGN=MIDDLE  ALT=\"+30+=+10x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to find \"x\" we will divide each side by \"10\"<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+30+=+10x+ ALIGN=MIDDLE  ALT=\"+30+=+10x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+30%2F10+=+10x%2F10+ ALIGN=MIDDLE  ALT=\"+30%2F10+=+10x%2F10+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3+=+highlight%2810%29x%2Fhighlight%2810%29+ ALIGN=MIDDLE  ALT=\"+3+=+highlight%2810%29x%2Fhighlight%2810%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3+=+cross%2810%29x%2Fcross%2810%29+ ALIGN=MIDDLE  ALT=\"+3+=+cross%2810%29x%2Fcross%2810%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3+=+x+ ALIGN=MIDDLE  ALT=\"+3+=+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+3+ ALIGN=MIDDLE  ALT=\"+x+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "(remember \"x\" is the time in hours), we can replace \"x\" with \"3\" in the second equation, to find \"y\"<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+90x+=+y+ ALIGN=MIDDLE  ALT=\"+90x+=+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+90%283%29+=+y+ ALIGN=MIDDLE  ALT=\"+90%283%29+=+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+270+=+y+ ALIGN=MIDDLE  ALT=\"+270+=+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+270+ ALIGN=MIDDLE  ALT=\"+y+=+270+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can check our two answers by replacing \"x\" and \"y\" in the first equation<BR>\n" );
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document.write( "x = 3<BR>\n" );
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document.write( "y = 270<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+500+-+100x+=+470+-+y+ ALIGN=MIDDLE  ALT=\"+500+-+100x+=+470+-+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+500+-+100%283%29+=+470+-+%28270%29+ ALIGN=MIDDLE  ALT=\"+500+-+100%283%29+=+470+-+%28270%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+500+-+300+=+470+-+270+ ALIGN=MIDDLE  ALT=\"+500+-+300+=+470+-+270+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+200+=+200+ ALIGN=MIDDLE  ALT=\"+200+=+200+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (True)<BR>\n" );
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document.write( "Here are the simplified equations with the numbers<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system+%28+100%285+-+3%29+=+470+-+270%2C+90%283%29+=+270%29+ ALIGN=MIDDLE  ALT=\"+system+%28+100%285+-+3%29+=+470+-+270%2C+90%283%29+=+270%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system+%28+100%282%29+=+200%2C+90%283%29+=+270%29+ ALIGN=MIDDLE  ALT=\"+system+%28+100%282%29+=+200%2C+90%283%29+=+270%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "If we look at the formula, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+rate%28time%29+=+distance+ ALIGN=MIDDLE  ALT=\"+rate%28time%29+=+distance+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system+%28+100%282%29+=+200%2C+90%283%29+=+270%29+ ALIGN=MIDDLE  ALT=\"+system+%28+100%282%29+=+200%2C+90%283%29+=+270%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This means that the car went 200 km at 100 km/h, and it went 100 km/h for 2 hours<BR>\n" );
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document.write( "The car went 270 km at 90 km/h, and it went 90 km/h for 3 hours<BR>\n" );
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document.write( "The distances add up to the total distance, as well as the time with the total time<BR>\n" );
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document.write( "The car went 200 km at 100 km/h<BR>\n" );
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document.write( "The car went 270 km at 90 km/h<BR>\n" );
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document.write( "Hope I helped, Levi<BR>\n" );
document.write( " </SPAN>\n" );
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