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## Homework Statement

An unstable sysemt may have two or more decay modes, with a Rate R

_{1}for decay through mode 1 and R

_{2}for decay through mode 2. Use the meaning of the rate to show that the total lifetime [tex]\tau[/tex] of the system is given by 1/[tex]\tau[/tex]=1/[tex]\tau[/tex]

_{1}+1/[tex]\tau[/tex]

_{2}.

## Homework Equations

## The Attempt at a Solution

## Homework Statement

## Homework Equations

## The Attempt at a Solution

I tried to manipulate the basic equation for decay, but I hit a dead end. I think the part I am stuck on is how to insert the fact that there are two different rates into the equation. Thanks