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Benone would finish mower garden in 8 hours. Pandele would finish in 10 hours mowing same garden. How long would finish mower garden together?

Sagot :

crisforp
In 1 hour, Benone _ _ _ g / 8 ;
In 1 hour, Pandele _ _ _ g / 10 ;
= = = = = = = = = = = = = = = = =
In 1 hour, Benone and Pandele  _ _ _ g / 8 + g / 10 = 5g / 40 + 4g / 40 = 9g / 40;
Benone and Pandele would finish garden together in 40 / 9 hours = 4 hours 26 minutes 40 seconds;
[tex]Benone-\frac{1}{8}\ mower\ garden\ per\ hour\\\\Pandele-\frac{1}{10}\ mower\ garden\ per\ hour\\\\\frac{1}{8}+\frac{1}{10}=(*)\\\\find\ LCD(\frac{1}{8};\ \frac{1}{10})\\\\List\ of\ the\ multiples\ of\ 8:0;\ 8;\ 16;\ 24;\ 32;\ \boxed{40};\ 48;...\\List\ of\ the\ multiples\ of\ 10:0;\ 10;\ 20;\ 30;\ \boxed{40};\ 50;\ ...\\\\LCD(\frac{1}{8};\ \frac{1}{10})=40\\\\\frac{1}{8}=\frac{1\cdot5}{8\cdot5}=\frac{5}{40};\ \frac{1}{10}=\frac{1\cdot4}{10\cdot4}=\frac{4}{40}[/tex]

[tex](*)=\frac{5}{40}+\frac{4}{40}=\frac{9}{40}-together\ per\ hour[/tex]

[tex]t-time\ when\ together\ finish\ the\ garden\\\\\frac{9}{40}\cdot t=1\ \ \ \ \ \ |multiply\ both\ sides\ by\ \frac{40}{9}\\\\\boxed{t=\frac{40}{9}\ (h)=4\frac{4}{9}\ h=4h+\frac{4}{9}h=4h+\frac{4}{9}h=4h+\frac{4}{9}\cdot60\ min\approx4h27min}[/tex]
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