Dear Sports Analysis Folks,

As I was practicing the other day, a couple of guys came over to see me. One of them, named Cheatin’ Chad, said that he thought I was pretty fast, probably faster than he is. "But if you gave me a head start, maybe as little as four meters, I bet I could beat you!"

The other guy, Snide Steve, was much more confident. "You’re fast – and certainly faster than Chad. But I am way faster than you. I could even wait a two full seconds after you started, and still beat you!"

What do you think? They challenged me to a 50 m race this Saturday. Who should I race? Cheatin' Chad, who needs a head start, or Snide Steve, who I know is faster than I am, but will give me a head start? Can I beat either one? They said they had used your services before, so maybe you have some data on them?

If I can beat Chad, what is the best head start I can give Chad and still win?

If I can beat Steve, what is the shortest time I can make Steve wait and still beat him?

Please let me know as soon as possible.

Sincerely,

Your athlete