Hectares

The tractor plows the first day of 4.5ha, the second day 6.3ha and the third day 5.4ha. It worked whole hours a day, and its hourly performance did not change and was the highest of the possible. How many hectares did it plow in one hour (what is it performance)?

Result

h =  0.9 ha/h

Solution:

a h=4.5 b h=6.3 c h=5.4  45=325 63=327 54=233 GCD(45,63,54)=32=9  x=GCD(45,63,54)=9  h=x/10=9/10=910=0.9  a=4.5/h=4.5/0.9=5 h b=6.3/h=6.3/0.9=7 h c=5.4/h=5.4/0.9=6 h  h=0.9=910=0.9 ha/ha \cdot \ h=4.5 \ \\ b \cdot \ h=6.3 \ \\ c \cdot \ h=5.4 \ \\ \ \\ 45=3^2 \cdot 5 \ \\ 63=3^2 \cdot 7 \ \\ 54=2 \cdot 3^3 \ \\ \text{GCD}(45, 63, 54)=3^2=9 \ \\ \ \\ x=GCD(45,63,54)=9 \ \\ \ \\ h=x/10=9/10=\dfrac{ 9 }{ 10 }=0.9 \ \\ \ \\ a=4.5/h=4.5/0.9=5 \ \text{h} \ \\ b=6.3/h=6.3/0.9=7 \ \text{h} \ \\ c=5.4/h=5.4/0.9=6 \ \text{h} \ \\ \ \\ h=0.9=\dfrac{ 9 }{ 10 }=0.9 \ \text{ha/h}



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