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*.

When they met, each had walked for the same length of time:d+ (d-200) =x(1) Hencex= 2d- 200

After the fight, Pete walked for 8 minutes:d/V= (d- 200)v(2)

(and Johnny for 18 minutes:d- 200)(V/2) = 8 HenceV= (d- 200)/4 (3)

By substituting the values ford(v/2) = 18 Hencev=d/9 (4)

4Henced/(d- 200) = 9(d- 200)/d

5Solving this quadratic in the classic way yieldsd^{2}- 3600d+ 360,000 = 0

However,d= 600 or 120 andx= 2d- 200 = 1000 or 40

The distance between the two bars is exactly 1000 meters.d= 600 andx= 1000

Source: Berrondom, Marie

Categories: Rates, Reasoning

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