Quadratic help!!

May 2010
7
0
Australia
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)
 

Grandad

MHF Hall of Honor
Dec 2008
2,570
1,416
South Coast of England
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.

Grandad