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A model hydroelectric power station produces just enough electric power to light a 6.0 W lamp. The model is found to be 80% efficient at converting the potential energy store of the water into electrical work. What is the input power of the water running through the pipes?

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AL2006

You said that the useful output power from the model is 6 watts.  You also said that the model is 80% efficient.  We have no reason to doubt your word, so we know that

(useful output) / (input power) = 80% or 0.8

(6 watts) / (input power) = 0.8

Multiply each side by (input power): 6 watts = (0.8) (input power)

Divide each side by 0.8 :  Input power = (6 watts/ 0.8)

Input power =  7.5 watts

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