document.write( "Question 557429: Harry takes 2 hours less to travel 50km than Cara takes to travel 35km. Cara travels at a speed that is 5km/hr slower that that of Harry. Find the time taken by Harry and Cara to complete their respective journeys and the speed at which they travelled. \n" ); document.write( "
Algebra.Com's Answer #362602 by rajagopalan(174)\"\" \"About 
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Let clara's speed=x
\n" ); document.write( "clara's time=35/x.........B
\n" ); document.write( "Harrys' speed=x+5
\n" ); document.write( "Harrys' time=50/(x+5)....A
\n" ); document.write( "given ...B-A=2
\n" ); document.write( "(35/x)-(50/(x+5)=2
\n" ); document.write( "taking LCM as x(x+5)
\n" ); document.write( "we get numerator ...35(x+5)-50x
\n" ); document.write( "we get denominator LCM x(x+5)
\n" ); document.write( "[35(x+5)-50x)]/[x(x+5)]=2
\n" ); document.write( "35x+175-50x=2x^2+10x
\n" ); document.write( "175=2x^2+25x
\n" ); document.write( "rewriting
\n" ); document.write( "2x^2+25x-175=0
\n" ); document.write( "find 2 numbers whose product is -350 ie(175*2) and their sum is 25
\n" ); document.write( "the numbers are -35 and 10 by factoring 350
\n" ); document.write( "2x^2+25x-175=0
\n" ); document.write( "2x^2+35x-10x-175=0
\n" ); document.write( "x(2x+35)-5(2x+35)=0
\n" ); document.write( "(x-5)(2x+35)=0
\n" ); document.write( "we get x=5 or -35/2
\n" ); document.write( "ignoring the negative value as speed can not be negative
\n" ); document.write( "we get x=5
\n" ); document.write( "verify
\n" ); document.write( "clara's time=35/x.........B=35/5=7 hrs
\n" ); document.write( "Harrys' time=50/(x+5)....A=50/10=5 hrs
\n" ); document.write( "B - A =7-5=2
\n" ); document.write( "ok\r
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