Math Help - Answer clarification: another race problem.

1. Answer clarification: another race problem.

A can run 1 km in 4 minutes 51 seconds and B in 5 minutes.
How many meters start can A give B in a Km race, so that the race may end in a dead heat?

There is a difference of 9 seconds between A and B.
A runs 30.8 meters in 9 sec so A has to give B a start of 30.8 meters.

But the answer says 30 meters. Can any one get 30 meters. Appreciate your help.

2. Re: Answer clarification: another race problem.

Hello, hisajesh!

I had to baby-talk my way through it . . .

$A$ can run 1 km in 4 minutes 51 seconds and $B$ in 5 minutes.
How many meters start can A give B in a 1 km race, so that the race may end in a dead heat?

$A$ runs 1000 m in 291 seconds.

$B$ runs 1000 m in 300 seconds.
His speed is: . $\tfrac{1000}{300} \,=\,\tfrac{10}{3}\text{ m/s.}$
In 291 seconds, $B$ runs only: . $\tfrac{10}{3}\times 291 \,=\,970\text{ m.}$

Therefore, $B$ should get a 30-meter headstart.

3. Re: Answer clarification: another race problem.

Just wondering why my style of solving gives an extra .8 meters.