# Solution #24: Bar Flies

Let x be the distance between the two bars.

Let d be the distance covered by Pete when he met Johnny.

Let V be Pete's speed and v be Johnny's speed before the fight.

The sum of the distances covered at the time they met is x.

```    d + (d-200) = x                            (1)
Hence x = 2d - 200
```
When they met, each had walked for the same length of time:
```    d/V = (d - 200)v                           (2)
```
After the fight, Pete walked for 8 minutes:
```    (d - 200)(V/2) = 8

Hence V = (d - 200)/4                          (3)
```
and Johnny for 18 minutes:
```    d(v/2) = 18

Hence v = d/9                                  (4)
```
By substituting the values for V and v into equation (2), we have
```    4d/(d - 200) = 9(d - 200)/d
```
Hence
```    5d2 - 3600d + 360,000 = 0
```
Solving this quadratic in the classic way yields
```    d = 600 or 120     and     x = 2d - 200 = 1000 or 40
```
However, d must be smaller than x, so only one solution is possible:
```    d = 600     and     x = 1000
```
The distance between the two bars is exactly 1000 meters.
Source: Berrondom, Marie
Categories: Rates, Reasoning
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