# Word problem on quad. equation

• September 28th 2009, 06:25 AM
Ilsa
on a journey of 250 km, a driver calculated that by increasing his average speed, by 5 km/h, he would take 25 minutes less. find his usual average speed , correct to 2 dec. places.

Ans: 52.33 km/h

i really need to know how to get this answer- i've tried by forming the quadratic equation:

250 - 250 = 25
x (x+5) 60

by keeping the speed as x.

pls help!
• September 28th 2009, 06:33 AM
stapel
What you've posted is actually a rational equation.

What did you get when you solved this equation?

Please be complete. Thank you! (Wink)
• September 28th 2009, 07:24 AM
reiward
$\frac{250}{x} - \frac{250}{x+5} = \frac{25}{60}$

$\frac{250}{x} - \frac{250}{x+5} = \frac{5}{12}$

remove the denominators
$\frac{250}{x} - \frac{250}{x+5} = \frac{5}{12} ] (12)(x)(x+5)$

$
(250)(12)(x+5) - 250(12)(x) = 5(x)(x+5)$

$3000x + 15000 - 3000x = 5x^2 + 25x$

$15000 = 5x^2 + 25x$

$5x^2 + 25x - 15000 = 0$(then simplify by dividing by 5)

$x^2 + 5x - 3000 = 0
$

Then I used the quadratic formula:

$x = \frac{-5 + \sqrt12025}{2}$

and

$x = \frac{-5 - \sqrt12025}{2}$

$x = \frac{-5 - 109.66}{2}$

$x = \frac{104.66}{2}$

$x = 52.33$

For the subtraction: REJECTED

$x = \frac{-5 - 109.66}{2}$

$x = \frac {-114.66}{2}$

$x = -57.33 (REJECTED)$