In a km race, if A gives B a 40 m start, A wins by 19 seconds, but if A gives B 30 seconds start, B wins by 40 m. Find the time that each takes to run a km?

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- Nov 8th 2012, 07:25 PMhisajeshRace and time problem.
In a km race, if A gives B a 40 m start, A wins by 19 seconds, but if A gives B 30 seconds start, B wins by 40 m. Find the time that each takes to run a km?

- Dec 20th 2012, 07:26 AMhollywoodRe: Race and time problem.
This is just algebra, isn't it? Let $\displaystyle t_A$ be A's time for a kilometer and $\displaystyle t_B$ be B's time for a kilometer. Then the first condition is:

$\displaystyle t_A = 0.96t_B - 19$

The second condition is:

$\displaystyle 0.96t_A = t_B-30$

So the solution is $\displaystyle t_B=150$, $\displaystyle t_A=125$, i.e. A takes 125 seconds to run a kilometer and B takes 150 seconds to run a kilometer.

- Hollywood - Jan 23rd 2013, 03:51 PMhisajeshRe: Race and time problem.
Sorry for the late response. can you explain in details how do you get to those equations.

- Jan 23rd 2013, 07:00 PMhollywoodRe: Race and time problem.
It's pretty much just translating the words to equations. It's actually not easy - you have to think about what's happening in these races:

"if A gives B a 40 m start, A wins by 19 seconds"

so A runs 1km in 19 seconds less time than B runs 0.96km

$\displaystyle t_A = 0.96t_B - 19$

"if A gives B 30 seconds start, B wins by 40 m"

so A runs 0.96km in 30 seconds less time than B runs 1km

$\displaystyle 0.96t_A = t_B-30$

- Hollywood