Thread: Word problem on quad. equation

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!

What you've posted is actually a rational equation.

What did you get when you solved this equation?

Please be complete. Thank you!

$\displaystyle \frac{250}{x} - \frac{250}{x+5} = \frac{25}{60}$

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

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

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

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

$\displaystyle 15000 = 5x^2 + 25x$

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

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

Then I used the quadratic formula:


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

and

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

For the addition:

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

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

$\displaystyle x = 52.33 $

For the subtraction: REJECTED

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

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

$\displaystyle x = -57.33 (REJECTED)$