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 $\displaystyle x$ kph. Then Marnie walks at $\displaystyle x+1$ kph.
Using the formula
$\displaystyle \text{time} = \dfrac{\text{distance}}{\text{speed}}$
Marnie takes $\displaystyle \frac{20}{x+1}$ hours, and Jon takes $\displaystyle \frac{20}{x}$ hours.
Since Jon takes $\displaystyle 1$ hour more than Marnie, we get:
$\displaystyle \dfrac{20}{x}=\dfrac{20}{x+1}+1$
Now multiply both sides by $\displaystyle x(x+1)$ to get rid of fractions:
$\displaystyle 20(x+1)=20x+x(x+1)$
$\displaystyle \Rightarrow 20x+20=20x+x^2+x$
$\displaystyle \Rightarrow x^2+x-20=0$
$\displaystyle \Rightarrow (x+5)(x-4)=0$
$\displaystyle \Rightarrow x = 4$, since $\displaystyle x=-5$ is impossible.
So Jon walks at 4 kph and Marnie at 5 kph.
Grandad