To solve for the outer planets, we have to look into how the Gunas from the Inner planets are transmuted to the outer planets. The physical principle of Conservation of Momentum is a good parallel here and we can write the following equation:

The conservation of momentum states that, the amount of momentum remains constant; momentum is neither created nor destroyed, but only changed through the action of forces.

We can translate this into an applicable equation as:

Inner [ Sum of GunasTattva ] = Outer [Sum of GunasTattva ]

Let us apply this first to the Akash Tattva. As the Akash tattva contains subtly, all the other elements [ Fire + Water + Air + Earth = Akash], for this transfer of quality we can write the equation as

Inner [ Sattvic (Fire) + Sattvic (Water) + Sattvic (Earth) + Sattvic (Air)] = Outer [Sattvic (Akash)]

As there are no inner Sattvic Air and Earth planets, and there is only one outer Sattvic (Akash) planet of Jupiter, the equation resolves to. Lagna, the source of Akash tattva, is ignored here as it is the recipient of Time.

Inner [Sattvic (Fire) + Sattvic (Water)] = Outer [Jupiter]

Inner [ Sun + Moon] = Outer [ Jupiter]

Or

Jupiter = [6 + 10] = 16

The Tamasic and Fire Element of Inner planet Ketu balances with the Tamasic Fire element of outer Mars

Inner [Tamasic (Fire)] = Outer [Tamasic (Fire)]

Or

Inner [Ketu] = Outer [Mars]

Or

Mars = 7

Kujavat Ketu!

As there are no inner Air (Vayu) planets, and there are no outer Rajas planets, there is no quality to transfer. This makes sense as the inner planets are composing our body with Water [Moon, Venus] and Earth [Mercury, Ketu] and enlivening it with Fire [Sun, Ketu]. Air is transient in our body and the primary cause of disease and aging of the body and thus relegated to the outer realms away from our body.

Thus, we have the following resolutions of outer planets MahaDasha durations of

Jupiter 16
Mars 7

If we were to now write the equation of the outer planets we get

Jupiter + Mars + Rahu + Saturn = 60

Or

16 + 7 + Rahu + Saturn = 60

Or

Rahu + Saturn = 37

Shanivat Rahu!

The integer resolution with the two numbers being close is 18 & 19 thus solving for Saturn and Rahu durations. Rahu is faster than Saturn as takes the lower number of 18.

This now gives us the full solution of the outer planets as