SOLUTION: Felice drove her car 300km at a certain average speed. Had she travelled 10kph faster, the trip would have taken 1 hour less. Find Felice's average speed.

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Question 980312: Felice drove her car 300km at a certain average speed. Had she travelled 10kph faster, the trip would have taken 1 hour less. Find Felice's average speed.
Answer by ikleyn(52884) About Me  (Show Source):
You can put this solution on YOUR website!

50 km%2Fh  and  60 km%2Fh.

I solved it momentarily without using equation  (mentally!)


OK,  this is a joke :)

Now let me solve it with using equations.

Let  x  be the Felice's average speed.
Then she spent  300%2Fx  hours to cover  300 km.

If she'd traveled  10 km%2Fh  faster, i.e.  x+%2B+10 km%2Fh,  then the trip would take  300%2F%28x%2B10%29,  and it would be in  1  hour less than  300%2Fx.  Thus you have an equation

300%2Fx - 300%2F%28x%2B10%29 = 1.

Solve this equation simplifying it step by step:

300*(x + 10) - 300*x = x*(x +10),

300x + 3000 -300x = x^2 + 10x,

x^2 + 10x - 3000 = 0.

Next, apply the quadratic formula  (see the lesson  Introduction into Quadratic Equations  in this site)
or the  Viete's theorem  (lesson  Solving quadratic equations without quadratic formula).

You will get this answer:  x = 50 km%2Fh.

Another root  (x = -60 km%2Fh)  is not applicable.