SOLUTION: A motorist travels from Town A to Town B which are 75km apart at an average speed of x kph.If he increases his average speed by 10kph,he would have reached Town B by 15 minutes ear

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Question 665713: A motorist travels from Town A to Town B which are 75km apart at an average speed of x kph.If he increases his average speed by 10kph,he would have reached Town B by 15 minutes earlier.Find the Value of x
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
speed x
speed x + 10

Distance = same 75 km
original time – time with increased speed =0.25 hour
t=d/t
75/x-75/(x+10)= 0.25
LCD= x ( x + 10 )
multiply by LCD
75(x+10)-75x=0.25x(x+10)
75x+750 -75x=0.25X^2+2.5x
750=0.25X^2+2.5x
0.25X^2 +2.5x-750 =0
Find roots of the quadratic equation
a= 0.25 b= 2.5 c= -750

x1=(-2.5+sqrt(6.25-750))/0.5
x1=( -2.5 + 27.5 )/ 0.5
x1= 50

x2=(-7-sqrt(49-20)/2
x2=( -2.5 - 27.5 )/ 0.5
x2= -60
Speed cannot be negative.
x= 50 km/h
m.ananth@hotmail.ca