Help with a piecewise function problem

Thehibby21

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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.
 
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.
You are missing the basic point of the exercise, which is to translate the specification of the problem from a natural language to the more precise and concise language of mathematical notation. Suppose I asked you what distance was covered in the first 1/2 hour, in the first hour, in the first two hours. I am pretty sure you can give the correct answer. So what is the formula for s if

\(\displaystyle 0 \le t \le 2.\)
 
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