# 'uniform rate': if the race is a tie, how long is the track?

##### Junior Member
here is another baffler

jan can run at 7.5 m/s and mary at 8 m/s. on a race track, jan is given a 25 meter head start. if the race is a tie, how long is the track

i have decided that jans rate is 7.5, and marys 8. the times are both n, but i need to figure out where the 25 goes.

#### stapel

##### Super Moderator
Staff member
If the total distance is "d", then what was the distance run by the one with the head start?

When you reply, please include your chart and everything else you have done on this exercise. Thank you.

Eliz.

##### Junior Member
Code:
|------|------|------|----------|
|      | rate | time | distance |
|------|------|------|----------|
| Jan  |  7.5 |   n  |  7.5n    |
| Mary |   8  |   n  | 8n + 25  |
|------|------|------|----------|
???

#### Denis

##### Senior Member
Not quite Sadsack, but good try: Mary's distance is simply 8n.

Then you solve with equation representing the differene of the 2 distances:
let's see what you can do...we're all pulling for you :wink:

##### Junior Member
wait..... would it be 8n-7.5n=25?

yes

oh. thanks!!!

#### soroban

##### Elite Member
Re: 'uniform rate': if the race is a tie, how long is the tr

Here's a back-door approach to this problem.

Jan can run at 7.5 m/s and Mary at 8 m/s on a race track.
Jan is given a 25 meter head start.
If the race is a tie, how long is the track?
Code:
      M           J
* - - - - - * - - - - - - - - - - *
25

Jan is 25 meters ahead of Mary.

Mary runs 0.5 m/s faster than Jan.
It is as if Jan is stopped and Mary runs to her at 0.5 m/s.

How long does it take Mary to cover the 25 meters?
. . It takes her: $$\displaystyle \frac{25}{0.5} \:=\:50$$ seconds.

In that time, Mary has run: $$\displaystyle 50\,\times\, 8\:=\:\fbox{400\text{ meters}}$$, the length of the track.