# Thread: Help with a piecewise function problem

1. ## Help with a piecewise function problem

I'm having trouble figuring out where to begin on this piecewise function problem and expressing a as a piecewise function of t.

A certain ironman triathlon consists of a 2.4 mile swim, followed by a 112 mile bike ride, and ends with a 26 mile run.
A contestant in this competition swims at a rate of 1.2 mi/hr., bikes at a rate of 14 mi/hr., and runs at a pace of 4 mi/hr.

Let t to be the number of hours since the contestant started the race, and let s=s(t) be the total distance covered at time t. Assume no time is lost in transition from one event to another.

2. ## Re: Help with a piecewise function problem

Originally Posted by Hibby21
I'm having trouble figuring out where to begin on this piecewise function problem and expressing a as a piecewise function of t
Do you mean $\displaystyle s$ and not $\displaystyle a$? So are you having trouble expressing $\displaystyle s(t)$ even on the first leg of the triathlon? If not, that's where you begin.