SOLUTION: 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 c

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.
Answer by rajagopalan(174) (Show Source): You can put this solution on YOUR website!
Let clara's speed=x
clara's time=35/x.........B
Harrys' speed=x+5
Harrys' time=50/(x+5)....A
given ...B-A=2
(35/x)-(50/(x+5)=2
taking LCM as x(x+5)
we get numerator ...35(x+5)-50x
we get denominator LCM x(x+5)
[35(x+5)-50x)]/[x(x+5)]=2
35x+175-50x=2x^2+10x
175=2x^2+25x
rewriting
2x^2+25x-175=0
find 2 numbers whose product is -350 ie(175*2) and their sum is 25
the numbers are -35 and 10 by factoring 350
2x^2+25x-175=0
2x^2+35x-10x-175=0
x(2x+35)-5(2x+35)=0
(x-5)(2x+35)=0
we get x=5 or -35/2
ignoring the negative value as speed can not be negative
we get x=5
verify
clara's time=35/x.........B=35/5=7 hrs
Harrys' time=50/(x+5)....A=50/10=5 hrs
B - A =7-5=2
ok

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