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

  • Thread starter NotASmurf
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B would need a head start of at least 20 meters to win the race against A. This is calculated by setting up a system of equations using the distance formula and solving for the head start needed.
  • #1
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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  • #2
Min 20 metres.
 
  • #3
Min?? Working out?
 
  • #4
Minimum of 20 metres.
 
  • #5
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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Thanks
 

1. How is the head start determined?

The head start is typically determined by the difference in speed between the two competitors. If A is faster than B, then B will need a larger head start in order to have a chance at winning the race.

2. Can we accurately predict the amount of head start B would need to win?

Yes, using mathematical equations and calculations, we can accurately predict the amount of head start B would need to win. However, this also depends on factors such as the distance of the race and the terrain.

3. Why does B need a head start to win?

B needs a head start because A has an inherent advantage in terms of speed. This head start helps to level the playing field and give B a fair chance at winning the race.

4. Is the amount of head start needed different for every race?

Yes, the amount of head start needed can vary depending on the specific conditions of each race. Factors such as the distance, terrain, and weather can all affect the amount of head start B would need to win.

5. Can B still win without a head start?

It is possible for B to win without a head start, but it would require A to slow down significantly or for B to have some other advantage such as a shorter distance to cover. In general, B would need a head start to have a fair chance at winning against A.

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