Derivation of the ETP formula

[puntosaurus]

Cracked it ! The equal time point is the the point where onward to the destination is the same time as return to the departure.

Using the symbols of the equation that means:

ETP/H = (D-ETP)/O (time = dist/speed)

so ETP/H = D/O - ETP/O (expanding RHS)

and ETP/H + ETP/O = D/O (adding ETP/O to both sides)

and (OETP + HETP)/OH = D/O (bringing the LHS to a common denominator)

so OETP + HETP = DOH/O = DH (multiplying by OH)

and ETP(O+H) = DH (factorising the LHS)

therefore ETP = DH/(O+H). QED.

Well it kept me happy for a couple of days !