Question

Cum se rezolva problema:Benone ar termina de cosit in gradina in 8 ore. Pandele ar termin de cosit aceeasi gradina in 10 ore. Daca ar cosi impreuna in cat timp ar termina ?

Answer 1

$Benone-\frac{1}{8} \ coseste \ intr-o \ ora \\\\ Pandele-\frac{1}{10} \ coseste \ intr-o \ ora \\\\\\ \frac{1}{8}+\frac{1}{10}= \ (1) \\\\ Aflam \ cel \ mai \ mic \ multimplu \ comun \ (\frac{1}{8};\frac{1}{10}): \\\\\\ Lista \ multiplilor \ pentru \ 8: \ 0; \ 8; \ 16; \ 24; \ 32;\ \boxed{40};\ 48;... \\Lista \ multiplilor \ pentru \ 10: \ 0; \ 10; \ 20; \ 30; \ \boxed{40}; \ 50;... \\\\C.M.M.M.C \ (\frac{1}{8};\frac{1}{10})=40$
$\frac{1}{8}=\frac{1*5}{8*5}= \frac{5}{40}; \ \ \ \ \frac{1}{10}=\frac{1*4}{10*4} =\frac{4}{40}\\\\ (1)=\frac{5}{40}+\frac{4}{40}=\frac{9}{40}-impreuna \ pe \ ora \\\\ t-timpul \ cand \ vor \ termina \ impreuna \ gradina \\\\ \frac{9}{40}\cdott=1 \ \ |(*\frac{40}{9}) \ Inmultim \ ambele \ parti \ cu \ \frac{9}{40} \\\\\\ \boxed{t=\frac{40}{9}(h)=4\frac{4}{9}h=4h+\frac{4}{9}h=4h+\frac{4}{9}\cdot 60min \approx 4h \ 27min}$