SOLUTION: Please help me solve the word problem: Jan can run at 7.5 m/s and Mary at 8.0 m/s. On a race track jan is given a 25m head start, and the race ends in a tie. How long is the trac

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Question 222250: Please help me solve the word problem: Jan can run at 7.5 m/s and Mary at 8.0 m/s. On a race track jan is given a 25m head start, and the race ends in a tie. How long is the track?
Found 2 solutions by rfer, MathTherapy:
Answer by rfer(16322) About Me  (Show Source):
You can put this solution on YOUR website!
overtake at .5m/s
25/.5=50 m

Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!
Please help me solve the word problem: Jan can run at 7.5 m/s and Mary at 8.0 m/s. On a race track jan is given a 25m head start, and the race ends in a tie. How long is the track?

Let the length of the track be T

Since Jan’s speed is 7.5 m/s, and since she was given a 25 m head start, then her distance to the finish line is T - 25, and her time to get to the finish line is %28T+-+25%29%2F7.5 secs.

Now, since Mary ran the entire length of the track, and since Mary’s speed is 8 m/s, then Mary’s time to get to the finish line is T%2F8 secs.

Since they finished tied, then they both arrived at the finish line at the same time, which gives us: %28T+-+25%29%2F7.5+=+T%2F8

8(T – 25) = 7.5T ------ Cross-multiplying

8T – 200 = 7.5T

8T – 7.5T = 200

.5T = 200

T = 200%2F.5 = 400

This means that the track is a highlight_green%28400%29 meter track.