Say I have three locations A,B,C and I have a person going from A to B and measure the time it takes. Same for B to C. Let the variance of the time it takes for the path AB be a and for BC b.
Is it then valid to say that the variance of the time it takes to get from A to C is equal to a + b?
Only if the travel times of AB and BC are uncorrelated.
For general random variables: $Var(X+Y)=Var(X)+Var(Y)+2Cov(X,Y)$.