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Jerry and Jim run a race of 2000 m. First, Jerry gives Jim

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Re: Jerry and Jim run a race of 2000 m. First, Jerry gives Jim  [#permalink]

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New post 13 Oct 2017, 16:34
"Jerry gives Jim a start of 3mins and is beaten by 1000m". If Jim runs 1000 (2000 - 1000) in less then 3 min - you could also think more than 1000m in 3 min (since Jerry is faster than Jim) them his speed is more than 333. Therefore he needs less than 6 min for 2000m. Only option is B.
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Jerry and Jim run a race of 2000 m. First, Jerry gives Jim  [#permalink]

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New post 27 Dec 2017, 15:56
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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Re: Jerry and Jim run a race of 2000 m. First, Jerry gives Jim  [#permalink]

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New post 28 Dec 2018, 16:59
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Re: Jerry and Jim run a race of 2000 m. First, Jerry gives Jim   [#permalink] 28 Dec 2018, 16:59

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