Thread: Race 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?

This is just algebra, isn't it? Let be A's time for a kilometer and be B's time for a kilometer. Then the first condition is:



The second condition is:



So the solution is , , i.e. A takes 125 seconds to run a kilometer and B takes 150 seconds to run a kilometer.

- Hollywood

Sorry for the late response. can you explain in details how do you get to those equations.

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


"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


- Hollywood