How to set up running total in cell?

Here is what I am trying to do. We have to keep a running total of our engine hours, so everyday at the end of the day I need my pilots to enter the time they flew but want a protected cell to count up based on what they input everyday. example

A19 = blank box to enter flight time for the day I.E. 1.5
A20 is a box that started with a number 1137.5 (this cell is protected so they can't change the number)

When they enter 1.5 in A19 I need A20 to update to 1139 and not be able to be minused, only added to. I.E they can't put a negative number in A19 and have it count backwards.

then when the next pilot comes in and enters his time for the day say
A19= 2.3
A20 should then be 1141.3

basically a running total but everytime I try to do any formula to do this I get errors. Would really appreciate any help that I can get
thanks