rate problem
Source: VTRMC 2009 P1
May 31, 2021
ratesalgebra
Problem Statement
A walker and a jogger travel along the same straight line in the same direction. The walker walks at one meter per second, while the jogger runs at two meters per second. The jogger starts one meter in front of the walker. A dog starts with the walker, and then runs back and forth between the walker and the jogger with constant speed of three meters per second. Let meters denote the total distance travelled by the dog when it has returned to the walker for the nth time (so ). Find a formula for .