Agirl goes to her friend's house, which is at a distance of 12 km. She covers half of the distance at a speed of x km/hr and the remaining at a speed of (x+2) km/hr. If she takes 2 hrs 30 minutes to cover the whole distance;find x.
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Avg speed = tot dist/tot time
Avg speed=2*a*b/a+b = 2*x*(x+2)/x+x+2 = x*(x+2)/x+1
x(x+2)/x+1 = 12/2.5
x(x+2)/x+1 = 4.8
[Either solve by cross-multiplying and then quadratic OR using trial and error by assuming values,x=4kmph]
4*6/5=4.8..Hence,the vlue of x=4 kmph
Quadratic:
x(x+2)= 4.8*(x+1)
x^2 + 2x = 4.8x + 4.8
x^2 - 2.8x - 4.8 =0
x^2+1.2x-4x-4.8=0
x(x+1.2) -4(x+1.2)=0
(x-4)(x+1.2)=0
Hence,x=4 kmph
Avg speed=2*a*b/a+b = 2*x*(x+2)/x+x+2 = x*(x+2)/x+1
x(x+2)/x+1 = 12/2.5
x(x+2)/x+1 = 4.8
[Either solve by cross-multiplying and then quadratic OR using trial and error by assuming values,x=4kmph]
4*6/5=4.8..Hence,the vlue of x=4 kmph
Quadratic:
x(x+2)= 4.8*(x+1)
x^2 + 2x = 4.8x + 4.8
x^2 - 2.8x - 4.8 =0
x^2+1.2x-4x-4.8=0
x(x+1.2) -4(x+1.2)=0
(x-4)(x+1.2)=0
Hence,x=4 kmph
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