SOLUTION: In mrs. kuehn's class wendy found out that her walking rate is 2 meters per second. When she gets home from school she finds times her younger sister jenny as jenny walks a hundred

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Question 378666: In mrs. kuehn's class wendy found out that her walking rate is 2 meters per second. When she gets home from school she finds times her younger sister jenny as jenny walks a hundred meters. Wendy figures out that jennys walking rate is 1.5 meters per second. Jenny challenges wendy to a walking race because wendy know she walks faster. She gives jenny a 20 meter head start hoping that jenny will win in a close race. How long should the race be if wendy wants it to end in a tie? how would i set this up as a linear equation?
Found 2 solutions by solver91311, mananth:
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Remember: Distance equals rate times time. But that means time equals distance divided by rate. We are given the rates and we want the times to be equal. So Jenny's race is described by:

And Wendy's race is described by:

And since for a tie we want Jenny's time and Wendy's time to be equal, so:

And solve for

John

My calculator said it, I believe it, that settles it

Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website!
let them race for a distance of x meters
..
Jenny gets a head start of 20 meters
.
so her distance is x-20 meters
..
Wendy walks x meters
..
Jenny's apeed = 1.5 m/second
wendy speed = 2m/second
..
If there has to be a tie ,they take same time.
...
t= d/r
..
Jenny's time = (x-20)/1.5
Wendy's time = x/2
..

cross multiply
1.5x=2(x-20)
1.5x=2x-40
-2x
1.5x-2x=-40
-0.5x=-40
/-0.5
x=-40/0.5
x=80 meters, the distance they have to race.
...
m.ananth@hotmail.ca