Question 106158
Let x=the original speed
____x+10=the increased speed


{{{speed=distance/time}}}
{{{time=distance/speed}}}

If a bus traveled 10 km/h faster, it would take 2h less time to make a 315km trip

time for the car traveling with its orig. speed={{{315/x}}}

time for the car with faster speed ={{{(315/(x+10))-2}}}


This means that:

{{{(315/x)+2=315/(x+10)}}}
{{{(x(x+10))((315/x)+2)=(x(x+10))(315/(x+10))}}}
{{{315(x+10)+2x(x+10)=315x}}}
{{{315x+3150+2x^2+20x=315x}}}
{{{2x^2+315x+20x+3150=315x}}}
{{{2x^2+335x+3150=315x}}}
{{{2x^2+335x-315x+3150=315x-315x}}}
{{{2x^2+20x+3150=0}}}
{{{x^2+10x+1575=0}}}

Using the quadratic formula,

{{{x=(-10+-sqrt(10^2-4*1*1575))/(2*1)}}}

The discriminant is negative------the roots are unequal and imaginary(see my lesson,"Don't discriminate the DISCRIMINANT!!!!!" and,

therefore, there is no solution!


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HyperBrain!