document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1009506>Question 1009506</A>: <I><SPAN STYLE=\"word-break: break-all;\"> uniform motion. a woman drives 10 miles, then increases her speed by 10 miles per hour and drives another 25 miles. find the original speed if she drove for 45 minutes </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #625004 by </B><A HREF=/tutors/aboutme.mpl?userid=addingup><B>addingup(3677)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=addingup><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=addingup><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=625004\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the original speed be x. Then, time it took to travel the first 10 miles<BR>\n" );
document.write( "= 10/x<BR>\n" );
document.write( "Then we increase the speed <BR>\n" );
document.write( "= (x+10) and since the distance at this speed is 25<BR>\n" );
document.write( "= 25/(x+10)<BR>\n" );
document.write( "Finally, the above is 10mph. But she only drove for 45 minutes. We can't have apples and oranges. We need to convert the 45 minutes to hours<BR>\n" );
document.write( "= 45/60= 0.75 hour <BR>\n" );
document.write( "---------------------------------------<BR>\n" );
document.write( "total time:<BR>\n" );
document.write( "= (10/x)+(25/(x+10))= 0.75 Put the fractions over a common denominator:<BR>\n" );
document.write( "= {(10(x+10))/(x(x+10)}+{25x/(x(x+10))}= 0.75 Combine into a single fraction:<BR>\n" );
document.write( "= (10(x+10)+25x)/(x(x+10))= 0.75Simplify. Distribute 10 over x+10:<BR>\n" );
document.write( "= (10x+100+25x)/(x(x+10))= 0.75 Add x on top:<BR>\n" );
document.write( "= (35x+100(/(x(x+10))= 0.75 Rewrite 0.75 as a fraction. 0.75= 3/4:<BR>\n" );
document.write( "= (35x+100(/(x(x+10))= 3/4 Cross multiply so we get rid of fractions:<BR>\n" );
document.write( "= 4(35x+100)= 3(x(x+10) Multiply on both sides to get rid of parentheses. Remember to multiply from the inside out, so on the right first x*x and x*10 and then 3*x^2 and 3*10x:<BR>\n" );
document.write( "= 140x+400= 3x^2+30x Let's set the equation to 0:<BR>\n" );
document.write( "= 140x+400-3x^2+30x = 0 Factor the left side (FOIL):<BR>\n" );
document.write( "= -((x-40)(3x+10))= 0 Multiply times -1:<BR>\n" );
document.write( "= (x-40)(3x+10)= 0 Split into 2 equations:<BR>\n" );
document.write( "x-40= 0 or 3x+10= 0<BR>\n" );
document.write( "x= 40 or 3x= -10 The answer we are getting on the right is negative, we are looking for a positive number. Our answer is on the left:<BR>\n" );
document.write( "Answer: x= 40 is the original speed<BR>\n" );
document.write( "J </SPAN>\n" );
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