Question

I’m trying to create a math problem and I’m not sure exactly what type of math I need to research to create the formula.

There are two contestants in a race. In round 1 contestant A’s goal is to preform a task as quickly as possible while contestant B’s goal is to make this task take as long as possible to complete.
The formula I’m trying to create needs to determine how long contestant B will need to wait before beginning Round 2. Meaning the Faster contestant A completes the task the more contestant B is penalized.

Can anyone point me in the right direction?

Answer 1

contestant A's time must be minimized
contestant B's time must be maximized

assuming the time taken to complete the tasks vary depending on some variable,
meaning contestant A's time is a function and so is contestant B's time

so draw 2 seperate graphs, find the maximum and minimum and add those together

as for the penalization part, no clue, why would B be penalized if his job is to take as much time as possible to complete the task

Answer 2

Thanks for reply. I may not have been very clear. Maybe this will help.

In round 1, CA will be trying to complete a task as quickly as possible while CB tries to slow CA down, making it take longer to complete. Meaning CB's goal is to make the task take as long as possible for CA.

You may have helped point me in the right direction though. It sounds like I'll need to run time trials and come up with an average time for the course. Example: Say the fastest time is 1 minute, the slowest time is 100 minuets, and the average time is 50 minutes.

This way if CB is able to slow CA down and cause them to take 75 minutes to complete the task, CB would only get a 25 minute penalty. Or if CA completed the task in 25 minutes CB would get a 75 minute penalty.

Does that sound like it should work?