question posed on yahoo's 'answers'

This question was asked on Yahoo's 'Answers' :-

"A particle A of mass 0.5kg is suspended by a vertical string. A particle B
of mass 0.4kg is suspended from A by means of another string. A force 10N is
applied to the upper string and the particles move upwards.
a) find the tension in the string and
b) the acceleration of the system"


I've been thinking about it, and havent really convinced myself that I'm
thinking about it in the right way...

If we just considered one mass for a minute, hanging by a single string,
then with no other forces present the tension on the string would be just
'mg' right? But if there was a second force acting upwards from the top of
the string then what would the tension in the string be then? Surely it
would be the sum of 'mg' and the upward force?

Is that right??