Quadratic help!!

**LaylaSam** · June 19th 2010, 10:11 PM

marnie can walk 1km/m faster the jon. She completes a 20km hike 1 hour before him. Write an equation and solve it to find there walking speeds.

i cannot seem to solve this ahh

plz help me

**Grandad** · June 19th 2010, 10:50 PM

Hello LaylaSam

Originally Posted by LaylaSam

marnie can walk 1km/m faster the jon. She completes a 20km hike 1 hour before him. Write an equation and solve it to find there walking speeds.

i cannot seem to solve this ahh

plz help me

Suppose that Jon walks at $x$ kph. Then Marnie walks at $x+1$ kph.

Using the formula

$\text{time} = \dfrac{\text{distance}}{\text{speed}}$

Marnie takes $\frac{20}{x+1}$ hours, and Jon takes $\frac{20}{x}$ hours.

Since Jon takes $1$ hour more than Marnie, we get:

$\dfrac{20}{x}=\dfrac{20}{x+1}+1$

Now multiply both sides by $x(x+1)$ to get rid of fractions:

$20(x+1)=20x+x(x+1)$

$\Rightarrow 20x+20=20x+x^2+x$

$\Rightarrow x^2+x-20=0$

$\Rightarrow (x+5)(x-4)=0$

$\Rightarrow x = 4$ , since $x=-5$ is impossible.

So Jon walks at 4 kph and Marnie at 5 kph.

Grandad

**LaylaSam** · June 19th 2010, 10:52 PM

Omg ur a genious!!!

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