#### 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)

MHF Hall of Honor
Hello 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 $$\displaystyle x$$ 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.