SOLUTION: another problem.. If a bus traveled 10 km/h faster, it would take 2h less time to make a 315km trip. What is its speed? Thanks!

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: another problem.. If a bus traveled 10 km/h faster, it would take 2h less time to make a 315km trip. What is its speed? Thanks!      Log On


   

Question 106158: another problem..
If a bus traveled 10 km/h faster, it would take 2h less time to make a 315km trip. What is its speed?
Thanks!
Answer by HyperBrain(694) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=the original speed
____x+10=the increased speed

speed=distance%2Ftime
time=distance%2Fspeed
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%2Fx
time for the car with faster speed =%28315%2F%28x%2B10%29%29-2

This means that:
%28315%2Fx%29%2B2=315%2F%28x%2B10%29
%28x%28x%2B10%29%29%28%28315%2Fx%29%2B2%29=%28x%28x%2B10%29%29%28315%2F%28x%2B10%29%29
315%28x%2B10%29%2B2x%28x%2B10%29=315x
315x%2B3150%2B2x%5E2%2B20x=315x
2x%5E2%2B315x%2B20x%2B3150=315x
2x%5E2%2B335x%2B3150=315x
2x%5E2%2B335x-315x%2B3150=315x-315x
2x%5E2%2B20x%2B3150=0
x%5E2%2B10x%2B1575=0
Using the quadratic formula,
x=%28-10%2B-sqrt%2810%5E2-4%2A1%2A1575%29%29%2F%282%2A1%29
The discriminant is negative------the roots are unequal and imaginary(see my lesson,"Don't discriminate the DISCRIMINANT!!!!!" and,
therefore, there is no solution!

Power up,
HyperBrain!