document.write( "Question 307801: Rachel allows hersef 1 hr to reach a sales appointment 50 mi away. After she has driven 30 mi, she realizes that she must increase her speed by 15 mph in order to get there on time. What was her speed for the first 30 mi? \n" ); document.write( "

Algebra.Com's Answer #220140 by mananth(16946) $\"\"$ $\"About$

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Rachel allows hersef 1 hr to reach a sales appointment 50 mi away. After she has driven 30 mi, she realizes that she must increase her speed by 15 mph in order to get there on time. What was her speed for the first 30 mi?\r
\n" ); document.write( "\n" ); document.write( "Let her initial speed be x mph\r
\n" ); document.write( "\n" ); document.write( "time taken if she traveled that speed for 30 km = 30/x\r
\n" ); document.write( "\n" ); document.write( "she increased her speed to by 15 mph\r
\n" ); document.write( "\n" ); document.write( "her new speed = x+15 mph
\n" ); document.write( "time taken by driving with new speed = 20/x+15 hours\r
\n" ); document.write( "\n" ); document.write( "Actual time taken = 30/x + 20/ x+15 hours
\n" ); document.write( "30/x + 20/ x+15 =1\r
\n" ); document.write( "\n" ); document.write( "lcm = x(x+15)\r
\n" ); document.write( "\n" ); document.write( "30(x+15)+20x= x(x+15)\r
\n" ); document.write( "\n" ); document.write( "30x+450 +20x= x^2 +15x\r
\n" ); document.write( "\n" ); document.write( "x^2+15x-30x-20x-450 =0
\n" ); document.write( "x^2-35x-450=0\r
\n" ); document.write( "\n" ); document.write( "x^2 -45x+10x-450=0
\n" ); document.write( "x(x-45)+10(x-45)=0\r
\n" ); document.write( "\n" ); document.write( "(x+10)(x-45)=0\r
\n" ); document.write( "\n" ); document.write( "x=-10 OR x =45\r
\n" ); document.write( "\n" ); document.write( "-10 is not valid\r
\n" ); document.write( "\n" ); document.write( "So she drove at 45 mph for 30 miles\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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