How much of a head start does B need to win the race?

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    Head Race
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Discussion Overview

The discussion revolves around a race scenario involving two runners, A and B, who have different speeds. The problem is to determine how much of a head start B would need to win a 50-meter race against A, who runs faster. The conversation includes mathematical reasoning and calculations related to the scenario.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant suggests that B would need a minimum head start of 20 meters to win the race.
  • Another participant questions the term "min" and asks for clarification on the calculations.
  • A further contribution provides a mathematical approach, defining the head start as 'x' and the time taken to complete the race as 't', leading to equations based on the distances and speeds of both runners.
  • The calculations provided indicate that with a head start of 20 meters, B would finish the race at the same time as A.

Areas of Agreement / Disagreement

There appears to be agreement on the minimum head start being 20 meters, as multiple participants affirm this figure. However, the discussion does not explore alternative calculations or viewpoints beyond this consensus.

Contextual Notes

The discussion relies on assumptions about constant speeds and does not address potential variations in running conditions or other factors that might affect the race.

Who May Find This Useful

Individuals interested in mathematical problem-solving, particularly in scenarios involving relative motion and speed calculations, may find this discussion relevant.

NotASmurf
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Hey all. Simple problem here. 2 people are running at 2 different speeds in a race 50m long (A at 5 m/s B at 3 m/s), A is clearly going to win, How much of a head start would B need to win?
(This isn't a homework problem I'm just wondering how long I have to wait for my movie to buffer before I should start watching it.)
 
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Min 20 metres.
 
Min?? Working out?
 
Minimum of 20 metres.
 
let the headstart be denoted by' x' and time taken to complete the race be 't'. Note that time will be same for A and B. Now, using the fact that
Distance traveled = Speed* time, we have
For A, 50= 5*t
For B, 50=x + 3*t
Solve these to get x=20, t=10
 
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