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.

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) (Show Source): You can put this solution on YOUR website!

50 and 60 .

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 hours to cover 300 km.

If she'd traveled 10 faster, i.e. , then the trip would take , and it would be in 1 hour less than . Thus you have an equation

- = 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 .

Another root (x = -60 ) is not applicable.

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