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

[NotASmurf]

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.)

 

[ishendra]

Min 20 metres.

 

[NotASmurf]

Min?? Working out?

 

[ishendra]

Minimum of 20 metres.

 

[ishendra]

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

 

[NotASmurf]

Thanks