ETP & PNR Question
 

For an assignment for an ATPL navigation subject we have been asked to consider a scenario where the pilot does not know these formulas and how they might develop the formulas from scratch to figure out their ETP (aka CP) and the PNR. The formulas are below.

ETP = (Total Distance x Ground Speed Home)
(Ground Speed Home + Ground Speed On)

PNR = (Safe Endurance x Ground Speed Home)
(Ground Speed Home + Ground Speed On)

I understand how to use these formulas and their application to flight planning/navigation and can provide worked examples of their use, but the question is asking for a walk through on how one might develop these formulae and I don't know how to approach the question.

If anyone has any insight into how both these formulae are developed it would me much appreciated.

D = total trip distance
O = groundspeed out
H = groundspeed home
E = safe endurance
x = distance to PNR/PSR
c = distance to ETP
For ETP
c/H = (D-c)/O
Oc = H(D-c)
Oc = HD-Hc
c(O+H) = DH
c = DH/(O+H)
For PNR
x/O + x/H = E
Hx + Ox = EOH
x(H+O) = EOH
x = EOH/(O+H)
time to PNR/PSR = x/O = EH/(O+H)

Thanks SFI145 that was the information I was after. Cheers.