When, how many times & how often (less's better) switch batteries to end up with 2 dead batteries?

Question

we have two mobile boxes with the same batteries inside (same capacity), but two different micro-controllers with different power consumption, the batteries are hot swap-able (switchable).

One micro-controller power consumption is a constant $M$ mAh, the second's is a constant $S$ mAh.

• in this case $M$ = 130, and $S$ = 35
• the batteries are identical
  • have capacity of $2800$mAh

Answer 1

Let the capacity of each battery be $C$. Your total lifetime is $\frac {2C}{M+S}$ hours from dividing total capacity by total consumption. Swap them halfway through in time, as $\frac C{M+S}$ hours.