Let t be jerry's time to complete the race. In t minutes, jim goes 1800-x meters where x represents how far he goes in 30 seconds.

jim goes x meters in 30 seconds, so proportionally he goes 6x meters when given a head start of 3 minutes. He has 2000-6x meters left to go. During that distance, jerry completed half the race so we can say jim goes 2000-6x meters in a time of t/2 minutes So he goes 4000-12x meters in a time of t minutes. From the first scenario, he also goes 1800-x meters in t minutes. So 4000-12x=1800-x

Solving for x gives 200 meters. So jim goes 200 meters in 30 seconds. Proportionally, he goes 2000 meters in 300 seconds or 5 minutes.

The fastest way to solve would be to realize jim has to go more than half the distance in 3 minutes. By the end the gap is 1000 meters so when jim went for 3 minutes the gap must have been more since jim is slower than jerry.

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