Wie lange dauert die Inventur?In einem Mathe-Test hatten wir folgende Aufgabe:
Ein Mitarbeiter würde für eine Inventur 4 Std. benötigen, ein anderer 3 Std. wie lange dauert die Inventur, wenn beide zusammen die Inventur durchführen?
Mein Denkansatz: Mittelwert 4+3 =3,5; 3,5 ÷ 2=1,75 Std. Wo ist der Denkfehler?
$${\frac{{\mathtt{1}}}{{\mathtt{4}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{3}}}} = {\frac{{\mathtt{7}}}{{\mathtt{12}}}}$$ => $${\frac{{\mathtt{7}}}{{\mathtt{12}}}}{\mathtt{\,\times\,}}{\mathtt{x}} = {\mathtt{1}}$$ =>
$${\mathtt{x}} = {\frac{{\mathtt{12}}}{{\mathtt{7}}}} \Rightarrow {\mathtt{x}} = {\mathtt{1.714\: \!285\: \!714\: \!285\: \!714\: \!3}}$$
$$\left({\frac{{\mathtt{1}}}{{\mathtt{4}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right){\mathtt{\,\times\,}}{\mathtt{x}} = {\mathtt{1}}$$ ; $$\left({\frac{{\mathtt{3}}}{{\mathtt{12}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{4}}}{{\mathtt{12}}}}\right){\mathtt{\,\times\,}}{\mathtt{x}} = {\mathtt{1}}$$ ;
$${\frac{{\mathtt{1}}}{{\mathtt{4}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{3}}}} = {\frac{{\mathtt{7}}}{{\mathtt{12}}}}$$ => $${\frac{{\mathtt{7}}}{{\mathtt{12}}}}{\mathtt{\,\times\,}}{\mathtt{x}} = {\mathtt{1}}$$ =>
$${\mathtt{x}} = {\frac{{\mathtt{12}}}{{\mathtt{7}}}} \Rightarrow {\mathtt{x}} = {\mathtt{1.714\: \!285\: \!714\: \!285\: \!714\: \!3}}$$
$$\left({\frac{{\mathtt{1}}}{{\mathtt{4}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right){\mathtt{\,\times\,}}{\mathtt{x}} = {\mathtt{1}}$$ ; $$\left({\frac{{\mathtt{3}}}{{\mathtt{12}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{4}}}{{\mathtt{12}}}}\right){\mathtt{\,\times\,}}{\mathtt{x}} = {\mathtt{1}}$$ ;