If a gearbox was quoted as having a speed ratio of 1:8, which statement is true?

In a gearbox with a speed ratio of 1:8, the relationship between the input and output speeds is determined by this ratio. A speed ratio of 1:8 means that for every one rotation of the input shaft, the output shaft makes eight rotations. Therefore, if the output speed is 8000 RPM, you can calculate the input speed by dividing the output speed by the speed ratio.

This means:

Input Speed = Output Speed / Speed Ratio

Input Speed = 8000 RPM / 8 = 1000 RPM

Thus, if the output speed is 8000 RPM, the input speed would indeed need to be 1000 RPM for the gearbox to maintain that speed ratio. This is why the statement is accurate and properly reflects the mechanics of the gearbox operation.