SOLUTION: Jan can run 7.5 meters per second, Mary at 8.0 meters per second. On a race track Jan is given a 25 meter head start, the race ends in a tie. How long is the track?

Question 375190: Jan can run 7.5 meters per second, Mary at 8.0 meters per second. On a race track Jan is given a 25 meter head start, the race ends in a tie. How long is the track?
Found 2 solutions by mananth, corncob:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Jan can run 7.5 meters per second, Mary at 8.0 meters per second. On a race track Jan is given a 25 meter head start, the race ends in a tie. How long is the track?
Jan 7.5 m/s
Mary 8m/s
..
let the track distance = x
Jan gets 25 m head start
..
Time taken is the same
..
time = d/r
(x-25)/7.5 = x/8
(x-25)*8=7.5x
8x-200=7.5x
8x-7.5x=200
0.5x=200
x=200/0.5
x=400 meters the track length
...
m.ananth@hotmail.ca
Answer by corncob(8) (Show Source): You can put this solution on YOUR website!
Here you see two variables...Jan who can run 7.5 meters per second and Mary who can run 8 meters a second. To figure out how long the trck is, if they tie, you will need to assign variables to help make the problem easier.
A good universal varibale to use is x. In turn, you goal is to try to find out what x is.
So assigning variables:
I would make Jan's 7.5 plus a head start into: 7.5x+25
Jan's wold be: 8x
distance of the track is:x
Then you set up an equation that would make then equil each other, because they tie.
A sample of the equation could be:
7.5x+25=8x
From there you will simplify the problem by getting all of the x's to one side.
7.5x+25-7.5x=8x-7.5x
YOu do it like this because when solving an equation, you have to do to each side the same thing...
then you have,
25=.5x
That is not finished because .5 is not what we are looking for, so you multiply 0.5x times 2 to get 1x
25*2=.5x*2
50=x
So the answer is 50 meters!
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