The first external pair has a 12-tooth driver and 36-tooth driven gear. On that intermediate shaft, a separate 15-tooth gear is fixed and drives a 45-tooth output gear. The input speed is 1,800 RPM. This is a two-stage compound train with two actual external meshes, not four independent shafts and not an idler sequence.
Calculate both stage ratios
Stage one is 36/12 = 3. Stage two is 45/15 = 3. These values describe speed reduction across each mesh. The two gears on the intermediate shaft share the same shaft speed, so there is no ratio or direction change between them; the second ratio begins only where the 15-tooth gear meshes with the 45-tooth gear.
Multiply and reduce the total
The total is (36/12) × (45/15) = 1,620/180 = 9. The output speed factor is the reciprocal 1/9, so 1,800 × 1/9 = 200 RPM exactly. GearTrain performs the integer multiplication and reduction before producing any decimal display, preserving the exact result even for stages that do not reduce individually to whole numbers.
Two reversals restore the input direction
The first external mesh reverses rotation on the intermediate shaft. The second external mesh reverses it again at the output, so the final shaft turns in the same ideal direction as the input. This parity result assumes exactly the two external meshes entered. An internal mesh, crossed-axis pair, idler, or different physical topology would require a different direction model.