14

Part of 2013 Stanford Mathematics Tournament

Problems(2)

2013 General Problem 14

Source:

Peter is chasing after Rob. Rob is running on the line

y=2x+5

2

units a second, starting at the point

(0,5)

. Peter starts running

t

seconds after Rob, running at

3

units a second. Peter also starts at

(0,5)

and catches up to Rob at the point

(17,39)

. What is the value of t?

SMT 2013 Team Test #14

Source:

You have a 2 meter long string. You choose a point along the string uniformly at random and make a cut. You discard the shorter section. If you still have 0.5 meters or more of string, you repeat. You stop once you have less than 0.5 meters of string. On average, how many cuts will you make before stopping?