SOLUTION: Jan can run at 7.5 m/s and Mary at 8.0 m/s. On a race track Jan is given a 25 m head start, and the race ends in a tie. How long is the track?

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Question 57404This question is from textbook Algebra: Structure and Method
: Jan can run at 7.5 m/s and Mary at 8.0 m/s. On a race track Jan is given a 25 m head start, and the race ends in a tie. How long is the track? This question is from textbook Algebra: Structure and Method

Found 2 solutions by Paul, funmath:
Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
Let x represent the length of the track
EQUATION:
7.5x+25=8x
0.5x=25
x=50
Hence, the track is 50m long.
Paul.

Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Jan can run at 7.5 m/s and Mary at 8.0 m/s. On a race track Jan is given a 25 m head start, and the race ends in a tie. How long is the track?
The formula for distance: highlight%28d=rt%29, where d=distance, r=rate, and t=time.
They ran the same amount of time:t
The race is the same distance for both: d
The distance Jan went is:d= 7.5t+25
The distance Mary went is: d= 8.0t
The equation to solve for time is is:
7.5t+25=8.0t
-7.5t+7.5t+25=-7.5t+8.0t
25=.5t
25/.5=.5t/.5
50=t
t=50 s
We were asked how long the race was, so plug t=50 s into Mary's distance equation:d= 8.0t
d=8.0(50) m
d=400 m
Happy Calculating!!!