document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=129756>Question 129756</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hi sir pls help me <BR>\n" );
document.write( " A motorist drove 2 hours at one speed and then for 3 hours at another speed . He covered a distance of 252Km. If he had travelled 4 hours at the first speed and 1 hour at the second speed , he would have covered 244Km . Find two speeds ?  ANS-[48 ,52] </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #94733 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=94733\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let his first speed be represented by x and his second speed be represented by y. Then recall that<BR>\n" );
document.write( "the distance covered is found by multiplying speed times the time spent traveling at that speed.<BR>\n" );
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document.write( "In the first case the motorist drove 2 hours at the first speed and 3 hours at the second speed.<BR>\n" );
document.write( "So the distance he traveled at the first speed is x times the 2 hours at that speed and <BR>\n" );
document.write( "is 2x km. And the distance traveled at the second speed is the rate y times the 3 hours that<BR>\n" );
document.write( "he traveled at that speed or 3y km. Add these two distances together and set them equal to the <BR>\n" );
document.write( "252 km he covered:<BR>\n" );
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document.write( "2x + 3y = 252<BR>\n" );
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document.write( "Similarly, had he traveled 4 hours at the first speed he would have gone a distance of 4x km.<BR>\n" );
document.write( "And had he then driven for 1 hour at the second speed he would have traveled 1*y or y km. Adding<BR>\n" );
document.write( "these two distances together are to result in a total distance of 244 km. In equation form this<BR>\n" );
document.write( "is:<BR>\n" );
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document.write( "4x + y = 244 km<BR>\n" );
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document.write( "So our equation set is:<BR>\n" );
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document.write( "2x + 3y = 252 and<BR>\n" );
document.write( "4x + y = 244<BR>\n" );
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document.write( "Multiply the top equation (all terms on both sides) by 2 and the equation set then becomes:<BR>\n" );
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document.write( "4x + 6y = 504<BR>\n" );
document.write( "4x + y = 244<BR>\n" );
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document.write( "Subtract these two equations in vertical columns. This will eliminate the 4x terms in each<BR>\n" );
document.write( "equation and you are left with:<BR>\n" );
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document.write( "5y = 260<BR>\n" );
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document.write( "Solve for y, the second speed, by dividing both sides of this equation by 5 and you get that<BR>\n" );
document.write( "the second speed is:<BR>\n" );
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document.write( "y = 260/5 = 52 km per hour<BR>\n" );
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document.write( "You can now solve for x, the first speed, by returning to either of the original equations and<BR>\n" );
document.write( "substituting 52 for y. Let's use the equation:<BR>\n" );
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document.write( "4x + y = 244<BR>\n" );
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document.write( "Substitute 52 for y and you have:<BR>\n" );
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document.write( "4x + 52 = 244<BR>\n" );
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document.write( "Get rid of the 52 on the left side by subtracting 52 from both sides to reduce the equation to:<BR>\n" );
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document.write( "4x = 192<BR>\n" );
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document.write( "Solve for x by dividing both sides by 4 and you have:<BR>\n" );
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document.write( "x = 192/4 = 48<BR>\n" );
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document.write( "So we know that the first speed that he traveled at in both trips was 48 km per hour, and the<BR>\n" );
document.write( "second part of both trips he traveled at 52 km per hour.<BR>\n" );
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document.write( "Hope this helps you to understand the problem.<BR>\n" );
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document.write( " </SPAN>\n" );
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