MathDB

You are racing an Artificially Intelligent Robot, called Al, that you built. You can run at a constant speed of

10

m/s throughout the race. Meanwhile, Al starts running at a constant speed of

1

m/s. Thereafter, when exactly

1

second has passed from when Al last changed its speed, Al’s speed instantaneously becomes

1

m/s faster, so that Al runs at a constant speed of

k

m/s in the kth second of the race. (Start counting seconds at

1

). Suppose Al beats you by exactly

1

second. How many meters was the race?

Problem Statement