Filling Jars to Measure Time

If water is flowing at the same constant rate through each of H ⩾3 hoses, so that any one hose will fill any one of J ⩾ 2 available jars in exactly one hour, then what are the fillable fractions of a jar, and what are the measurable fractions of an hour? Learning to systematically answer such questions will not only equip readers to fluently use fractions, but also introduce or reintroduce them gently to the Queen of Mathematics – Number Theory.