• Jun 19th 2010, 10:11 PM
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 (Headbang) plz help me (Speechless)
• Jun 19th 2010, 10:50 PM
Hello LaylaSam
Quote:

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 (Headbang) plz help me (Speechless)

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.