How to divide standard deviation

#1
Hi,

I am developing a model of vehicles traveling regular routes. Assume the length of the path (distance) from each stop to the next is known. Assume the mean travel time is known from each stop on the route to the next. Further assume the standard deviation for the mean travel time from each stop to the next is also known. Finally, assume every part of every route is similar to every other and variations in travel time are perfectly random.

Now, if a vehicle is between two stops, is it reasonable to assume that the mean travel time to the next stop is?

Mn = Mpn * (Dn / Dpn)

where,

Mn = mean time from current location to next stop
Mpn = mean time from previous stop to next stop
Dn = distance to next stop
Dpn = distance from previous stop to next stop

Can the standard deviation be treated similarly? That is, if the bus 3/4 of the way from stop A to stop B and the standard deviation of the travel time from A to B is S, then is it reasonable to assume the sd of the travel time for the remaining 25% of the path will be .25*S ?

Thanks for any help you can offer.

Regards,
Matt