Question

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

Answer 1

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;

Answer 2

`Benone-(1)/(8)\ mower\ garden\ per\ hour\\\\Pandele-(1)/(10)\ mower\ garden\ per\ hour\\\\(1)/(8)+(1)/(10)=(*)\\\\find\ LCD((1)/(8);\ (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((1)/(8);\ (1)/(10))=40\\\\(1)/(8)=(1\cdot5)/(8\cdot5)=(5)/(40);\ (1)/(10)=(1\cdot4)/(10\cdot4)=(4)/(40)`


`(*)=(5)/(40)+(4)/(40)=(9)/(40)-together\ per\ hour`


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