Question

3 muncitori pot face o lucrare in 4 zile. Primul muncitor poate termina singur aceasta lucrare in 10 zile, iar al doilea in 12 zile.In cate zile ar termina aceasta lucrare al treilea muncitor?

Answer 1

    
$M_1 \;termina \; in \;10\;zile\;=\ \textgreater \ \;\;in\;4\;zila\;va\;termina\;\; \frac{4}{10}\;\;din\;lucrare. \\ M_2 \;termina \; in \;12\;zile\;=\ \textgreater \ \;\;in\;4\;zila\;va\;termina\;\; \frac{4}{12}\;\;din\;lucrare. \\ M_3 \;termina \; in \;x\;zile\;=\ \textgreater \ \;\;in\;4\;zila\;va\;termina\;\; \frac{4}{x}\;\;din\;lucrare. \\ \\ \frac{4}{10}+\frac{4}{12}+\frac{4}{x}=1 \\ \\ \frac{2}{5}+\frac{1}{3}+\frac{4}{x}=1$


$\frac{4}{x}=1-\frac{2}{5}-\frac{1}{3}= \frac{15}{15} -\frac{6}{15}-\frac{5}{15}= \frac{15-6-5}{15} =\frac{4}{15} \\ \\ =\ \textgreater \ \;\;\frac{4}{x}=\frac{4}{15} \\ \\ x= \frac{15*4}{4} = \boxed{15\;zile}$