FUN solving Quadratic equations

[sillybilly]

FUN solving Quadratic equations :)

Homework Statement

Marnie can walk 1km/h faster than Jon. She completes a 20 km hike 1 hour before him. Write an equation ans solve it and find their walking speeds.

Homework Equations

speed= distance/time
the quadratic equation

The Attempt at a Solution

i don't no how to start :(

but i no that for Marnie: S= D/T
and Jon S= D/T-1 because he's an hour slower.

 

[HallsofIvy]

Be careful- "S" has two different meanings in those equations while "D" and "T" mean the same thing! You should never use one symbol to represent two different things. Instead, since we are told that "Marnie can walk 1km/h faster than Jon", let's use S to represent Jon's speed so that Marnie's speed is S+ 1. Now those two equations are
S+ 1= D/T and S= D/(T-1). Further, we are told that D= 20 km so we actually have

S+ 1= 20/T and S= 20/(T- 1).

One thing you could do is use the second equation to substitute for S in the first:
20/(T-1)+ 1= 20/T. Multiplying both sides of the equation by T(T- 1) gets rid of the fractions and gives 20T+ T(T-1)= 20(T- 1)= 20T- 20, a quadratic equation in T. Solve that equation for T and use S+ 1= 20/T to find S.

That is slightly "inefficient" in that you have to solve for T first when the problem does not ask for T. Another way to do this would be to solve the first equation for T, by inverting to get T/20= 1/(S+ 1) so that T= 20/(S+ 1). Put that into the second equation to get S= 20/(20/(S+1)+ 1). That's a harder equation to solve but gives S directly.

 

[sillybilly]

ohh wow... thankyou soo much and yes the first one was easier :)
(i did them both)
THANK YOU SOOO MUCH :D